Police Scotland has condemned Rangers for failing to ask fans to return home after they gathered in Glasgow for title celebrations.
A senior officer said there had been a "lack of support" from the club despite repeated requests from police.
Earlier Deputy First Minister John Swinney also criticised Rangers for a "lack of leadership".
Rangers insisted its fans had been urged to follow the lockdown guidelines.
Large numbers of supporters flouted Covid rules to gather at Ibrox Stadium and Glasgow's George Square on Sunday after the club won the Scottish Premiership.
Officers made 28 arrests and handed out fixed penalty notices for a variety of offences including assaulting police officers, sectarian-related breaches of the peace, breaking Covid rules, and use of pyrotechnics.
Police later said no officers were injured and confirmed those arrested were aged 18 to 44.
Deputy Chief Constable Malcolm Graham said the behaviour of some supporters was "disgraceful".
He added: "I also strongly condemn the lack of support from Rangers Football Club over the messages we repeatedly asked them to put out to persuade fans not to go out celebrating and encourage those who did gather in large numbers to return home.
"We've been planning for the conclusion of the football season for some time since the league was allowed to resume and the sport is in a very privileged position given the restrictions seen across the country for almost a year.
"It was very clear through the lack of messaging that Rangers did not take seriously their responsibilities in terms of seeking to persuade their fans to celebrate safely and responsibly."
Deputy First Minister John Swinney condemned the scenes as "an absolute disgrace" which had undermined recent progress against the virus.
He said Rangers had been reminded of the need for fans to adhere to the restrictions by the Scottish government and Police Scotland during meetings on 26 February and 5 March.
"The Scottish government will be making our extreme disappointment at the lack of leadership clear to the team management."
Mr Swinney acknowledged that the title win was a "special moment" for the club and praised those fans who celebrated at home but he said it was "shameful" to see so many people deliberately flouting the rules.
"Events like yesterday risk spreading the virus and they show no regard or respect at all for the millions of households across Scotland who have stuck to the rules, who have not been able to meet up with friends and family to fully celebrate birthdays and other milestones or, in some case, attend funeral services of their loved ones," he said at the government's coronavirus briefing.
Under current Scottish government coronavirus guidance, public gatherings are banned and a maximum of two people from two households are allowed to meet outdoors.
➡️ George Square Memorial Benches— Glasgow City Council #StayHome (@GlasgowCC) March 8, 2021
We’ve had cleansing and parks teams in George Square since Sunday night, clearing debris and assessing the damage to furniture and plants. (1/9) pic.twitter.com/wekDZDbNtP
Glasgow City Council said a number of memorial benches donated by grieving relatives were damaged in George Square, and that it was working to trace the families.
The council promised that the benches, one of which was apparently in memory of a 10-year-old girl, would be restored.
A crowdfunding appeal to pay for the repairs, set up by the owner of the Louden Tavern at Ibrox Stadium, quickly raised its £5,500 target, with any extra funds being donated to the Anthony Nolan cancer charity.
Crowds of fans took to the streets after the game. Some let off flares while others chanted and waved flags outside the club ground, while supporters also gathered in George Square to celebrate.
Rangers issued a statement on Monday, in which the club said it had "proactively engaged" with its local MP, the justice minister, the Scottish government, Police Scotland and the SPFL in a bid to to maintain "a cohesive message regarding public safety during the Covid-19 pandemic".
The statement continued: "We understand the jubilance of our support across the world who recognise this has been a historic year for the club.
"Nevertheless, it has been of great frustration for all football fans across the world that they have not been able to watch their team within stadiums, especially for the loyal Rangers season-ticket holders who have stood by this football club through thick and thin in the last decade.
"We reiterate the message from our manager, Steven Gerrard, who highlighted that fans should adhere to government guidelines - stay safe, socially distance and look after each other in this difficult time."
On Twitter, the statement was accompanied by a clip of Gerrard from Friday's pre-match press conference.
The club said it was aware that there could be more "significant milestones" this season, and would "continue to proactively engage with key stakeholders to maintain a cohesive message in relation to government guidance at this present time".
However, Mr Swinney said messaging from the club on Sunday could have helped diffuse the situation and disperse the crowds.
"I think it would have been the duty of Rangers to say clearly and simply to fans that they shouldn't have come out to celebrate and when they did they should have gone home," he said.
"The silence from Rangers was deafening - that's a matter of profound regret."
Scotland's chief medical officer Dr Gregor Smith warned there was a "real risk" the celebrations would lead to a spike in Covid infections in the coming weeks.
He added: "It was quite demoralising to see so many people coming together.
"I am sure my colleagues across the NHS who at this stage in the pandemic are pretty exhausted felt the same way when they saw so many people mixing so freely without distancing or masks."
Last May thousands of Liverpool fans flouted social distancing guidelines and gathered outside Anfield to celebrate the club's first Premier league title in 30 years.
And in November hundreds of Celtic supporters defied the level four restrictions and converged on Celtic Park to call for the removal of the club's then manager Neil Lennon.