Police Scotland has criticised the "lack of support from Rangers Football Club" over failing to order thousands of fans who gathered in Glasgow yesterday to go home.
Fans congregated in George Square and outside Ibrox Stadium 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.
Deputy Chief Constable Malcolm Graham said: "The behaviour which we saw at the weekend was disgraceful and I utterly condemn the individuals who chose to completely disregard the coronavirus regulations, putting both the wider community and our officers at risk.
"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."
He added: "I commend the officers who delivered a policing operation which was entirely consistent with our approach throughout this pandemic to maintain public safety and minimise disorder, disruption and damage to property.
"They did this faced with considerable danger, all of which was completely unnecessary and avoidable.
"Where large numbers of people gather at an unplanned event such as this, we use established crowd control measures to ensure we are keeping the public safe and manage those who are refusing to disperse.
"We will work with football clubs, local authorities and the Scottish Government to ensure we do everything we can to persuade people that none of these scenes can be repeated as the football season continues."
Scotland's First Minister Nicola Sturgeon has condemned celebrations in Glasgow as "infuriating and disgraceful" after thousands of fans flouted the coronavirus lockdown to gather in the streets and celebrate Rangers winning the Scottish Premiership yesterday.
The mass gatherings have been widely condemned, with the First Minister warning that the celebrations could jeopardise plans to ease the coronavirus restrictions.
Scotland's Justice Secretary and police chiefs also urged rule-breakers to go home, but the pleas went unheeded, with fans packed into George Square and congregating outside Ibrox stadium to celebrate their first top-flight title in ten years.
Shortly after 5pm, Police Scotland said a "small number" of arrests had been made and officers at the scene were attempting to encourage fans to return home.
But by 8pm, the crowds had not dispersed, despite the police herding hundreds of people away from the stadium along Paisley Road West earlier in the evening.
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".
The club tweeted or retweeted 52 times in the six hours after they were crowned champions, but had not addressed the mass gathering of fans.
Ms Sturgeon had previously offered her congratulations to Rangers and said: "I congratulate @RangersFC on the title win & recognise what a moment this is for fans.
"But gathering in crowds just now risks lives, and could delay exit from lockdown for everyone else.
"If those gathering care at all about the safety of others and the country, they will go home."
Justice Secretary Humza Yousaf also asked fans to stay at home.
He wrote on Twitter: "I understand Rangers fans will be desperate to celebrate but please remember you must stay at home.
"No mass gatherings are allowed. We cannot risk any further spread of the virus."
Mr Yousaf warned that "UEFA will also be paying close attention as the Euros are around the corner".
Hampden Park in Glasgow is due to host some games of the delayed 2020 European Championships in the summer.
Meanwhile, police in Northern Ireland are investigating reports of large crowds of Rangers' supporters on the Shankill Road in Belfast last night.
People were pictured filling the area, despite a ban on public gatherings under coronavirus restrictions, to celebrate the Glasgow side's first title in a decade.
The Police Service of Northern Ireland has indicated that "appropriate enforcement action" will be taken.
Superintendent Nigel Henry said officers received reports of a street party and flares and fireworks being set off on the Shankill Road, as well as fireworks in the Ballysillan Road area.
He described the scenes as "disappointing".
"The numbers involved in the scenes last night were clearly a breach of the Health Protection (Coronavirus) Regulations, which is so disappointing when we know so many other people are adhering to the regulations and playing their part to keep people safe," he said.
"An investigation is under way, and appropriate enforcement action will be taken in relation to breaches of the regulations."
Northern Ireland has been living under a strict raft of rules aimed at stemming the spread of the virus since a spike of cases in December.
DUP MP Gregory Campbell urged fans not to break Covid-19 rules yesterday.
He said it would be a bad day for Rangers supporters if the title celebrations ended with people in intensive care beds.
"No-one is more delighted than myself to see this success for the Gers. It's been a long road. But so has the battle against Covid," he said.
"I understand the desire for celebrations but that doesn't justify breaking the public health rules.
"There will be plenty of time to celebrate in due course when the vaccine has been rolled out."
Sinn Féin MP Paul Maskey said: "Large crowds gathered in public, with no adherence to social distancing or mask wearing.
"These scenes were deeply concerning in the midst of a pandemic.
"Reports of sectarian chanting are also worrying and need to be investigated.
"I will be raising questions directly with the PSNI around their approach to these organised gatherings."
