The minister said putting a firm timeline on the initial inquiry was impossible when he was asked by his Labour shadow Margaret Curran whether the first conclusions could be published before Christmas.
Updating MPs on the crash, Mr Carmichael said the response of passers-by, including Labour MP Jim Murphy, had shown Glasgow at its best.
Ms Curran joined with cross-party tributes in the wake of Friday night's incident, which is thought to have killed nine people, including two police officers and a civilian pilot on the aircraft.
Mr Carmichael said: "With regard to the publication of the early report of the Air Accidents Investigation Branch (AAIB), it would be impossible to give any undertakings at the moment.
"I can say the earliest possible publication of the interim report will be made and I would very much hope, in the course of the investigation, any information that is able to supplied to the families will be supplied and should there be any difficulties in that regard then my office ... will stand ready to address these issues."
Mr Carmichael said of the 32 injured in the crash, 12 remain in hospital, including three in intensive care.
In his statement to MPs, Mr Carmichael said the Westminster Government would continue to work with the Scottish Government and Glasgow City Council in the aftermath of the crash.
And he added: "Investigations of this sort are inevitably complex and can be lengthy. I know all those affected will be looking for answers but the gathering of evidence especially at this early stage will be vital to that investigation.
"I hope the police and other investigatory agencies will be given the time and space to do their job."
Mr Carmichael said he had visited the scene of helicopter crash earlier today and met with representatives of the emergency services.
He said: "I'm sure the House will wish to recognise the outstanding work of the emergency services for the speed, professionalism and courage of the response on Friday night and Saturday morning.
"Police, fire and ambulance all responded magnificently working in difficult and dangerous circumstances. In particular, we should recognise police officers had to respond in circumstances where they were dealing not just with the death of members of the public but also with two of their own colleagues - Pc Kirsty Nelis and Pc Tony Collins."
But Mr Carmichael said "some of the most remarkable stories of courage and selflessness" emerged from reports of the response of ordinary members of the public, whether staff or customers in the Clutha, or passers-by.
He said: "They responded with no thought for their personal safety."
Paying tribute to Mr Murphy, the MP for East Renfrewshire who is in the Philippines on parliamentary business today, Mr Carmichael added: "He happened to be one of the first on the scene... he had been characteristically understated in describing his role but I'm sure I speak for the whole House when I say his response which was instinctive did him credit."
Mr Carmichael said he had been given a badge in Glasgow today bearing the slogan "People make Glasgow".
He told MPs: "The response of the people who make Glasgow has demonstrated all the courage and character that has made that city famous throughout the world.
"We in this House and the people we represent in communities throughout the United Kingdom stand in solidarity today with the people of Glasgow as they mourn their loss and start to come to terms with their grief.
"People make Glasgow. Today I wear that badge with pride."
Ms Curran said: "This has been a dark weekend for Glasgow and for our whole country. Where we should have been hoping to celebrate St Andrew's Day on Saturday, we were instead met with unexpected tragedy.
"When I attended the mass on behalf of Her Majesty's opposition in St Andrew's Cathedral on Saturday, yards from the site, there was a real sense of shock.
"I have lived all my life in Glasgow and I know when we hurt we grieve together and we mourn together. Today, all of Glasgow and all of Scotland are united in grief."
Ms Curran tributes to the emergency services who responded on Friday night and those still working at the site today.
She added: "Our minds are still focused on those who died and suffered injuries but we must establish what happened on Friday to prevent such tragedies in the future. You noted in your statement the air accident investigation has begun.
"Can I ask if you can tell us if we can expect this before Christmas?"
Labour's Pamela Nash (Airdrie and Shotts) told the Scottish Secretary: "Understandably it's taking a lot of time to safely and thoroughly search the Clutha ... but sadly this leaves many families in limbo at the moment.
"Can I ask you if you've had assurances that the emergency services had all the equipment and expertise they required to ensure that there wasn't anyone left in the Clutha alive in the immediate aftermath of the crash?"
Mr Carmichael replied he did not believe the emergency services were under-resourced and would be "astonished" if that was the case.
He added to Miss Nash: "It will of course be an ongoing investigation now which will require a very delicate and detailed search and I know, I completely understand the difficulties and the frustration that will cause for many people who still remain anxious and wait for news of their loved ones.
"I would say, however, in the long term what we all want is to get to the truth of the matter and I know from my own former professional experience, having worked at the Crown Office and Procurator Fiscal Service at an early stage of my career, that the early stages of evidence-gathering are of the most important and can have a significant bearing on the ability to establish the causes of these incidents.
"So I've no reason to believe and nobody suggested that there was any under-resourcing of the emergency services operation and I would be astonished in fact if that did turn out to be the case."
Conservative Bob Stewart, a former British Army colonel, said he was deeply saddened by what had happened in his father's home city.
Mr Stewart (Beckenham) told Mr Carmichael: "Will you agree with me, whatever happened to that helicopter, the pilot would have tried his level best to put it down safely and it was probably a traumatic incident which disallowed him from putting it into the river or on a flat piece of ground?"
Mr Carmichael replied it would be ill-advised for him to speculate.
He told Mr Stewart: "You have a distinguished service history which doubtless informs your views."
Labour's Tom Harris (Glasgow South) asked Mr Carmichael: "Does the Government or indeed the air accident investigators have a view on the policy in terms of risks versus values of police helicopters taking part in routine air patrols over densely populated areas rather than being deployed to deal with specific incidents?"
The Scottish Secretary replied: "That, essentially, in my view, would be an operational matter for the chief constable of Police Scotland, who would of course be accountable for his decision to the justice secretary in the Scottish Government."
Mr Carmichael also paid tribute to the courage and character of the people of Glasgow in the aftermath of the helicopter accident which claimed at least nine lives.
The city's response to the tragedy is "a very thin silver lining in a very dark cloud", the UK Government minister said.
Mr Carmichael spoke after visiting emergency services at the command centre at the site of Friday night's accident in which a police helicopter landed on the Clutha pub in Glasgow.
He then met with Glasgow City Council leader Gordon Matheson and signed a book of condolence set up in the council's headquarters.
"It's a very thin silver lining in a very dark cloud, but I think the response of the community in Glasgow has been absolutely magnificent," Mr Carmichael said.
"Adversity often brings out the best in people. I don't think there are any communities in the world that would respond in the way Glasgow has responded and is responding."
Mr Carmichael, wearing a badge that said "People Make Glasgow", said the slogan "summed up the response you saw late on Friday night into the early hours of Sunday morning".
He said: "Glasgow is no stranger to tragedy, we have seen it over the years. But the response of the people of the city I think has spoken volumes about the strength of the community and its courage and character."
People would want answers about the cause of the crash but the investigations may take some time.
"Time spent now taking care in the investigation will pay dividends at a later stage," he said, adding that he has "every confidence" that both the Air Accidents Investigation Branch and police will fulfil their roles "completely professionally".
But the Orkney and Shetland MP said his experience both as a solicitor and "as a Member of Parliament who has had helicopter tragedies take place in my own constituency in Shetland" show that such investigations are complicated and take time.
"The natural instinct of people who are grieving is to want to know how they lost their loved one. I would say though your best chance of knowing that is if as much evidence is gathered from the scene now which can then be evaluated and investigated and assessed at a later stage," he said.
"If it is possible for information to be shared with families as the investigation progresses then I hope it will be, but at the same time there would be no purpose served by putting ill-considered conclusions out into the public domain. You can see how that could end up causing even more pain to the grieving. Informed answers are what we need."
He told how he learned of the crash when civil servants texted him on Friday night. Since then he has been in contact with UK Transport Secretary Patrick McLoughlin and with the Prime Minister's office, saying: "The Prime Minister has made it very clear that if any assistance, either at strategic or operational level, is required by Police Scotland, that can be provided by a police force south of the border then they will have it."
Shadow Scottish secretary Margaret Curran accompanied Mr Carmichael during the visit to the command centre and to the council.
Ms Curran, who represents Glasgow East, said "there is a real sense of shock" in the city and stressed the need to "pull together as a city and keep the city together as we face the tragedy and try to support those who have lost their loved ones, support their families and make sure the services are working well".
She said: "I'm a Glasgow MP. I'm a Glaswegian. The city has been amazing. This is Glasgow where, in the deepest tragedy, we rally to support each other. But it is hard times and the city is hurting. We have to move on, move on to asking some of the questions about why this happened and what we do now."
Scottish Labour deputy leader Anas Sarwar, MP for Glasgow Central, also signed the book of condolence.
"It's been a sad few days but although we've seen the most tragic of scenes, we have also seen the best of our citizens, the way the people of Glasgow have come together, with passers-by coming to support the emergency services who were so brave in getting the situation under control, putting their own lives on the line as they did so," he said.
"A time will come when people will want to know more detail about what happened, but I think it's right in the short term we focus on making sure we're giving people the support they need."
A silent queue formed at Glasgow City Chambers as members of the public came to sign the book of condolence.
Among them was Kevin Lynch, 39, from Airdrie, a trainer with a charity which helps young people into training and employment.
"We have some of the young people with us, and they wanted to come down here and pay their respects. Everybody has been coming in this morning feeling rather sombre, rather down and depressed.
"We talked amongst ourselves, my colleagues and I, and we felt it was it was fitting we pay our respects, both as an organisation and ourselves as well."
Another one who came to sign the book was 17-year-old Levi McDonald from Rutherglen.
"I just wanted to pay my respects for the loved ones of the victims," he said.