Thirteen people were arrested for alleged public order offences in Glasgow on Saturday, and have since been released pending further action.
MSPs, QCs and independent legal advisers have joined football fans in accusing the police of "harassment, victimisation and disproportionate actions", Labour MSP Michael McMahon told Holyrood.
He was joined by fellow Labour MSP Hugh Henry in calling for an independent inquiry to ensure that the Offensive Behaviour at Football Act is not being used to "harass football fans".
Meanwhile, SNP MSP John Mason, whose constituency includes Celtic Park, has called for tougher policing around football stadiums to address public drinking and urination.
Mr MacAskill said Strathclyde Police may provide "a more accurate picture" of Saturday's events, said to involve members of the Celtic-supporting Green Brigade, supported by CCTV evidence when it is made public.
He said the Act has an 84% success rate in securing convictions and that he is delighted that action is being taken against the Glasgow Rangers fans recorded singing allegedly sectarian songs at a recent match against Berwick Rangers in England.
"A procedure introduced by the Labour-Liberal Democrat administration in 2006 requires an application for a submission to march to be submitted to the local authority no later than 28 days before any event," Mr MacAskill said.
"It was the right decision then and I believe it is the right decision today that local authorities should decide and police should monitor.
"If the Green Brigade put in an application, I have no doubt that many of the councillors who have expressed views would have been able to support it an lay down appropriate conditions for it.
"If we don't do that, we will have difficulties because there was also anticipation on Saturday to be a Scottish Defence League (SDL) demonstration commemorating the death of young Kriss Donald, which caused great grief for his family."
The murder of 15-year-old Kriss by an Asian gang in 2006 has become an unwelcome cause celebre for anti-immigration groups such as the SDL.
Mr MacAskill said: "In relation to events in Glasgow on Saturday, no such application was received. Strathclyde Police would be happy to brief elected members on recent events, which may give a more accurate picture of all the circumstances.
"Full video footage of the event cannot be released at the moment due to its role in criminal proceedings. This will again provide a fuller picture of all the circumstances surrounding Saturday's events.
"That footage will also be available to elected members at the conclusion of proceedings.
"None of the charges emanating from Saturday relate to the Offensive Behaviour at Football Act. They relate to matters such as the misuse of drugs, breach of the peace or other public order matters."
Mr McMahon said: "I had a meeting yesterday with the Chief Superintendent in Glasgow about the issues that were raised on Saturday. Can I congratulate the Cabinet Secretary on using the same deflection that police used yesterday with me."
Mr McMahon said Saturday's protest was held "because of concerns about the implementation of police actions in football grounds and outside football grounds, which has been deemed unfair and disproportionate".
He said: "I met with Celtic fans last night who are asking for an inquiry into what happened on Saturday so that everyone can be satisfied that this Act is not being administered in the way that people feel.
"Lawyers, academics and football fans have raised concerns that the Act and the policing of it is failing to tackle the problem of sectarianism, and is in fact raising tensions and being counter-productive.
"Sadly, it is now being widely alleged by not only fans but QCs and independent legal advisers who attended on Saturday that the event was met with the very harassment, victimisation and disproportionate actions by the police which the fans were protesting against in the first place.
"The proposed procession may well have been outwith the regulations outlined by the Cabinet Secretary but the complaints which have emanated from the actions of the police in dealing with it should shock and alarm this chamber."
Mr Henry said: "It has been suggested that the legislation is being used to harass football fans, not to deal with illegal behaviour. The Cabinet Secretary would be foolish to ignore these growing complaints.
"Will he act and order an inquiry with a report to this Parliament before large sections of football supporters lose confidence in the police?"
But Mr MacAskill said: "I have every confidence in the police and I recall that there was a live game coming from Berwick at which Rangers were playing in recently, at which sectarian singing was clearly audible and a matter of great complaint. I am delighted to say that it would appear that some action has been taken by the police.
"We do believe that the Act is working well, with 84% of those dealt with under it convicted, and I think Scottish football is a better place for it."
Mr McMahon said after the exchanges: "We need an inquiry because there are so many unanswered questions arising from events on Saturday. The Government and the police have tried to turn this into a separate issue from the Act.
"You can't do that because the protest was about that Act and about the heavy handed treatment of ordinary football fans at the hands of the police, so the issues are interlinked."
Mr Mason, SNP MSP for Shettleston which includes the stadium in Parkhead, said: "Many of my constituents want a stronger level of policing around football matches. They are fed up with their driveways being obstructed, they are fed up with alcohol being drunk in the streets and they are fed up with people urinating in public."
Mr MacAskill said: "There is a minority who do cause the considerable difficulties that John Mason makes a good point in drawing attention to, but I attended a football match on Sunday (the St Mirren V Hearts league cup final) that was well behaved and was a credit to both fans, and that's how we want to see football enjoyed."