Fans congregated in George Square and outside Ibrox after Rangers took their first top-flight title in 10 years.
Police made 28 arrests and seven people were issued with fixed penalty notices or will be reported to the Procurator Fiscal.
Reasons for arrest included assaulting police officers, breaching coronavirus regulations, disorder, use of flares and sectarian breaches of the peace.
In a statement released on Tuesday, Mr Livingstone said: “Across the weekend, thousands of Rangers supporters in Glasgow participated in spontaneous and intense mass gatherings. This should not have happened given the continuing public health crisis.
“Experienced officers, highly skilled in public order management, took appropriate steps to manage these challenging circumstances to protect people and minimise disruption to communities.
“Officers and staff worked, as they have done throughout this pandemic, with impartiality, professionalism and selfless commitment to public service. They have my personal support and I thank them for all that they do to protect their fellow citizens.
“Policing has stepped forward to take on additional responsibilities to support the significant restrictions on people’s freedoms of movement and association introduced by Parliament to combat the spread of coronavirus and save lives.
“Overall, across the last 12 months, the co-operation and support of the people of Scotland has been remarkable. I am very grateful for those who continue to demonstrate personal responsibility.
“I’ve been clear from the beginning of this pandemic that the strong relationship of trust policing has with our communities, underpinned by the principle of policing by consent, would be vital to the critical role officers and staff play in supporting the public health imperative.
“That’s why in April last year I commissioned John Scott QC to lead additional, independent and expert scrutiny of our policing response. I’ve been grateful for his Independent Advisory Group’s valued insight and challenge since it was established, including on the issue of mass gatherings and protests.
“I have asked Mr Scott to consider the events of the weekend at the next scheduled IAG meeting on Friday, 12 March, having regard to the fundamental human rights principles of legality, necessity and proportionality, and to consider any relevant issues for the policing of future events over the coming months.
“A number of senior officers, including those involved in the policing operation at the weekend, were already scheduled to attend this meeting. As has been the case throughout the last year, policing will benefit from the significant value the IAG brings to our thinking and operational practice.”
At the coronavirus briefing on Monday, Deputy First Minister John Swinney branded the behaviour of some Rangers fans an “absolute disgrace”.
He said: “To see so many people deliberately flouting [coronavirus] rules with no regard for the safety of others is shameful.
“Events like yesterday risk spreading the virus and show no regard or respect at all for the millions of households across Scotland who have been sticking to the rules, who haven’t been able to meet up with friends and families to fully celebrate birthdays and other milestones or, in some cases, to attend funeral services of their loved ones.”