The supporters had been suspected of planning an unauthorised protest march against an anti-sectarianism law.
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.
Justice Secretary Kenny 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 cilhbre 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."