The peer said key questions over why no further action was taken after accusations emerged were for the police, not the Liberal Democrats.
Lord Steel, who was also the first presiding officer at Holyrood, also said he would not have recommended Sir Cyril for a knighthood if he had known about his behaviour.
Police have announced that they are to investigate claims there was a cover-up of widespread sexual abuse at a school linked to the late politician.
Lord Steel said that he had become aware of the allegations about Sir Cyril's behaviour before he became an MP following an article in Private Eye imagine in the 1970s.
He said he had discussed the issue with Sir Cyril at that stage.
The former Rochdale MP pointed out that the article also included the information that police had investigated and no further action had been taken.
Lord Steel told the BBC: "Now one of the things that should come out now is why no action was taken?
"I think that's a legitimate public interest question, but it's not a question for the Liberal Democrats, it's a question for the police."
He added that although there had been Westminster gossip about Sir Cyril after the 1979 article: "We're a political party, not a detective agency, and idle gossip is not a basis for any inquiry at all.
"My basic point is that not a single story emerged - not even a rumour emerged - about him misbehaving as an MP.
"If that had happened, of course we would have inquired."
Lord Steel confirmed that he confronted Smith about allegations of abuse at a residential school in Rochdale when they were raised in the press in 1979, but took no further action after learning that the police had already investigated the claims.
The allegations related to a time in the 1960s when Smith was a Labour councillor and had not yet entered Parliament, and the Liberal leader had "no locus" in the affair, Lord Steel told BBC Radio 4's World at One.
"We are a political party, not a detective agency," said the peer, who led the Liberals as David Steel from 1976-88 before the merger with the SDP to form the Liberal Democrats.
But he said he would not have recommended Smith for a knighthood in 1988 if he had had "the slightest inkling" of allegations that he abused young men while an MP.
Lord Steel has come under pressure to explain his actions in relation to Smith since the launch of investigations by Rochdale Council and Greater Manchester Police into historic claims of physical and sexual abuse by the 29-stone politician, who was Labour mayor of Rochdale in the 1960s and Liberal MP for the town from 1972-92 before dying in 2010.
The peer said that his only knowledge of the allegations against Smith came in 1979 when Private Eye magazine reported on an investigation published by the Rochdale Alternative Press which detailed claims made by a number of young men about Smith spanking boys.
Lord Steel said: "All I knew was what was in Private Eye. Any member of the public could know that.
"I said to him `What's all this in Private Eye?' He said: `Yes, the report is true'. The Private Eye story said that the police had investigated and no further action had been taken.
"We have to remember that this was a different era. Corporal punishment was permitted. It would be totally illegal now, there is no question he would be up for assault now. In those days it went on."
Lord Steel said that he found Smith's reported behaviour "odd", but added: "The fact is these were allegations that were 10-15 years old. Since then - and after the closure of one of the institutions - he had gone on to be elected mayor of the town, he was awarded the MBE by the Labour Party for services to local government.
"I had no locus in the matter at all. He wasn't even a member of my party at that time."
Asked if he had considered launching an internal party inquiry, Lord Steel replied: "Why should I? There was no allegation about his behaviour as an MP.
"There are now allegations which have come to light since his death. These were very serious, but they were not known to us at the time."
Lord Steel said that the Private Eye report led to "gossip and tittle-tattle" in the Commons about Smith, but insisted that there was no firm allegation about his behaviour as an MP.
"Idle gossip is not a basis for any inquiry at all," he said.
"Not a single story emerged, not even a rumour emerged about him misbehaving as an MP. If that had happened, of course I would have inquired.
"If I had had the slightest inkling that that was going on, of course I would have taken action, but these were old allegations, publicly acknowledged, which the police had investigated."
Lord Steel said it was for the police and not the Liberal Democrats to explain why no action was taken on the initial allegations.
"The reports said it had been properly investigated by the police and no action had been taken," he said.
"One of the things that should come out now is why was no action taken? I think that is a legitimate public interest question but it is not a question for the Liberal Democrats, it's a question for the police."
World at One interviewed a former member of Rochdale Young Liberals, who said that Smith abused him after recruiting him to the party as a teenager in 1979.
"Cyril would say 'Let's go and do some door-knocking' and he would take me out on a drive on the moors above Rochdale and he would start putting his hand on my groin and fondling," said the man, speaking under condition of anonymity.
"I was shocked. I just froze. I had never had a sexual experience. The first time, it was something alien to me."
The man said Smith later groped him in the House of Commons after inviting him to Parliament: "He was introducing me to someone and then his hand started in the groin area. Obviously, they didn't see him, they couldn't have done because they wouldn't have allowed it. I felt awful. I had nightmares."
Lord Steel said that he was "quite happy" in 1988 to recommend Smith for a knighthood following his lengthy service in Parliament.
But he told World at One: "If I had had the slightest inkling that there was anything wrong in his behaviour it wouldn't have happened."
Another man told the programme that his parents had invited Smith - then a councillor - to speak to him after he got into trouble with the police in the 1960s.
"He said he wanted to discipline me and he would take me in the front room and talk to me," said the man, speaking anonymously. "After a couple of times, he said `What I want to do is smack your bottom'. He tried on a number of occasions to pull my pants down and put me over his knee and smack my bottom.
"On the third time, he said to me 'I'm going to do this now because you've been a naughty boy. If you don't let me do this, one of us is going to die'. He said he would kill me before he let me stop him. Those were his exact words."
Asked if Smith should have been prosecuted, Lord Steel said: "It sounds as though he should have been, yes, and certainly if these things happened today he would undoubtedly be prosecuted.
"A man is innocent until proved guilty. I hope these current inquiries will lead to some conclusion. I think the victims deserve to have their questions answered."