Police Scotland arrested 28 people after thousands of Rangers fans gathered in Glasgow on Sunday to celebrate winning the Scottish Premiership.
A further seven people were issued with fixed penalty notices or will be reported to the Procurator Fiscal.
Fans packed into George Square and gathered outside Ibrox Stadium after Rangers took their first top-flight title in 10 years.
The force said action was taken for offences including assaulting police officers, breaching coronavirus regulations, disorder, use of flares and sectarian breaches of the peace.
Chief Superintendent Mark Sutherland, divisional commander for Greater Glasgow, said: “Despite the coronavirus regulations and the prohibition of gatherings, our officers were faced with a very difficult set of circumstances as many thousands of supporters gathered to celebrate across a number of different venues.
“Our priority was public safety and this included reducing the risk of disorder, road safety and effective crowd management among the complexities of a vociferous crowd. This included established crowd control measures to prevent serious disorder in multiple areas and protect the public.
“An appropriate policing response was in place throughout the day and officers continually engaged and encouraged compliance with coronavirus regulations.
“Over the course of the day a number of minor injuries were sustained by members of the public, some of which were as a result of intoxication.”
“In total, 28 people were arrested and seven people were issued with fixed penalty notices or will be the subject of a report to the Procurator Fiscal.
“I am grateful to our officers who showed great commitment and professionalism throughout the course of the day, many of whom put their own health at risk during a challenging set of circumstances.”
He said the police operation was pre-planned.
Some politicians had criticised the police response, with Scottish Green MSP Ross Greer tweeting: “Expect Police Scotland to explain pretty quickly to Parliament why they decided to facilitate rather than disperse multiple mass gatherings during a national lockdown today.”
The SNP’s Sandra White posted on Twitter: “I’ll ask once again Chief Constable Livingstone what are Police doing? My constituents should not have to put up with this behaviour.”
Ms Sturgeon tweeted: “I share folks’ anger at this.
“Everyone has made so many sacrifices in the past year and seeing a minority risk our progress is infuriating and disgraceful.
“It is deeply unfair to the entire country, and the police have a hard enough job already.
“Please ask fans to go home @RangersFC”.
Justice Secretary Humza Yousaf also asked fans to stay at home, saying he understood they would be “desperate” to celebrate but must adhere to lockdown rules.
He warned Uefa would be paying “close attention” as Glasgow’s Hampden Park is due to host some games of the delayed 2020 European Championships in the summer.
David Hamilton, chairman of the Scottish Police Federation, which represents rank and file officers, said he was “appalled” by the scenes on Sunday.
He told BBC Good Morning Scotland: “We go on a model of policing by consent and that requires us to essentially deal with people on the basis that they’re prepared to do these things, particularly in vast numbers, and clearly in this case we were up against the tide here where thousands of people wilfully disregarded the health advice and were selfishly congregating in George Square, putting themselves at risk, their friends at risk, the supporters at risk and the police officers who were looking after after them at risk.”
He said that almost all of the officers on duty will not yet have been vaccinated and he is concerned for them.
Mr Hamilton said: “We’ve got a lot of people in jeopardy now and that’s just down to the selfishness of those who decided that celebrating their club’s victory was more important than the health of the country.”
Scottish Labour leader Anas Sarwar warned fans of the dangers they posed to themselves and their families by not adhering to the lockdown restrictions.
Speaking on Monday, he said: “Please, for your sake, for your safety and your family’s safety, please observe the social distancing rules, please do not have mass gatherings – this is to protect you and your loved ones and your family members.
“So, please, if you’re continuing those celebrations, please do them at home, please do them remotely. But do not risk the lives of yourselves, of your family members and your wider circles at the same time – it really isn’t worth it.”