The First Minister’s scathing attack on the club’s supporters came in the wake of scenes of violence in central Glasgow on Saturday.
National clinical director Jason Leitch separately warned the extended period of lockdown restrictions in Glasgow could last more than a week after the city was told it would stay at level three on Friday.
He also advised people to hug “cautiously” as much of the rest of Scotland prepares to move to level two restrictions from today.
More than five police officers were injured – at least one seriously – during the scenes in George Square on Saturday, with the Scottish Police Federation reporting broken bones and the “worst violence” in two decades of policing.
At least 28 people have been arrested in relation to the celebrations on Saturday, Police Scotland said, with deputy chief constable Will Kerr stating that “many more arrests” would follow.
Taking to Twitter to respond to the violence and gatherings in Glasgow after thousands of fans marched from Ibrox to George Square to celebrate Rangers’ Scottish Premiership title victory, Ms Sturgeon also called out the “vile anti-Catholic prejudice” witnessed.
She posted: “I’m understandably inundated with messages about yesterday’s disgraceful scenes in Glasgow. Police still have a job to do, which restrains my comments to some extent – but to say I’m utterly disgusted by the Rangers fans who rampaged through the city would be an understatement.
“I’m also angry on behalf of every law-abiding citizen. In normal times, the violence & vandalism, & the vile anti-Catholic prejudice that was on display would have been utterly unacceptable. But mid-pandemic, in a city with cases on the rise, it was also selfish beyond belief.”
The First Minister also called on Rangers FC to “reflect” on what the club can do to “tackle this behaviour”.
She said: “People across the country still living under the most difficult restrictions – not able to see family or attend weddings and funerals – are rightly furious at the irresponsible actions of a thuggish minority who seem to care little for the risks they pose to other people.
“Understandably people ask questions about if/how government and police can do more to prevent/tackle scenes like these and there is a need to reflect. That said Police Scotland officers have my admiration & thanks for the job they did in difficult and dangerous circumstances.
“I hope Rangers FC will also reflect on what more must be done to tackle this behaviour by fans, albeit a minority. However, ultimate responsibility lies with those who behaved in such a thuggish, sectarian and selfish manner. And that’s why we must let the police do their job.”
Rangers FC did not respond to a request for comment from The Scotsman.
The violence comes just two months after similar scenes in Glasgow when Rangers mathematically secured the title on the first weekend of March.
The scenes led to similar denouncement, but Police Scotland refused to release correspondence with the Scottish Government, the SPFL and Rangers FC on the plans to police the celebrations, instead releasing 17 pages of heavily redacted emails.
Justice secretary Humza Yousaf at the time labelled the celebrations “shameful”.
He took to Twitter on Sunday morning to post: “My full support to police officers who put in an incredible shift yesterday in very difficult circumstances.
"[It was] absolutely disgraceful that they were subjected to the kind of thuggery we saw last night.
"Incidents of violence, disorder, anti-Catholic and any other hatred will be followed up.”
Chair of the Scottish Police Federation, David Hamilton, said fans showed a “blatant disregard” for the safety of the public and frontline police officers as the general secretary of the police officer’s union criticised the SNP’s record around policing and criticised politicians passing on no more than “warm words”.
Speaking to BBC Radio Scotland on Sunday, Mr Hamilton said: “[I’m] absolutely appalled. The way things unfolded throughout the day is depressing and it’s almost speechless to see that number of people blatantly ignoring all the advice, the health advice, the government advice, the police advice, even the club advice to come together.
“And then for that to escalate when police officers tried to disperse to the levels of violence we experienced is just absolutely appalling.
"I think it was predictable as soon as the league started because somebody was always going to win the league and there is always going to be some kind of celebration in some part of the country.
"It was all about a matter of mitigation. Policing in this country is, of course, done by consent and the whole strategy throughout the coronavirus pandemic has been about making sure that people take that personal responsibility and they have not done so.”
In a statement, the Scottish Government confirmed it had held talks with Police Scotland, Glasgow City Council and Rangers FC, but would not be drawn on the nature of those discussions or whether politicians had attempted to persuade the police to take a stricter approach with supporters.
It also did not answer a question as to whether it had taken a different approach with the key organisations involved in the policing operation when compared to the similar scenes in early March.
A Scottish Government spokesperson said: “The Scottish Government, Police Scotland, Glasgow City Council and Rangers Football Club have held various discussions and worked closely together in the run up to Saturday. The message has been very clear that supporters should not gather, and we worked to ensure preparations were as robust and thorough as possible.
“We will liaise with Police Scotland and the football authorities to consider what further action can be taken.”
Assistant chief constable Gary Ritchie, from Police Scotland, said organisations and the club had urged supporters to take “personal responsibility for their actions” and criticised the “selfish decision” to gather at Ibrox and George Square.
He said: “There is no easy way to stop that number of people who are intent on coming into a city from doing so without causing significant disruption to everyone else.
“Our policing approach will always be to manage a crowd in a situation like this, and minimise disruption to the wider public, while keeping everyone safe.
“Policing a situation like this requires balance and a proportionate response. The level of force we use is dictated by the actions of the crowd.
"Sending in public order officers too early, particularly when a crowd is largely peaceful, can have the opposite effect and actually trigger violence and disorder.
“I strongly condemn the behaviour of these supporters who not only placed our officers at risk, but damaged the image and reputation of Glasgow, especially during this critical period of the pandemic.”
Speaking on the BBC’s The Sunday Show, Prof Leitch also criticised the actions of the fans.
He said: “It is so disappointing to see people break rules in whatever setting and for whatever reason.”
Discussing the decisions to keep Scotland’s largest city in level three, Prof Leitch said: “Certainly the toughest we’ve had to give advice about for months and months.
“It was really down to the wire on what was the right thing to do, but we’ve learned in Scotland and around the world that acting fast and hard always works.
“Delay rarely works and that is why we gave the advice we did.”
Asked if the outbreaks were likely to spread to other areas, he said: “I think we should watch and be cautious and careful.
“We have decided, with advice, that on Monday the rest of the country is safe to move to the next stage.
“But we all said the hugging, the increased hospitality, that should all be done very cautiously.
“So don’t go crazy, but we think it can be kept under control.”
Prof Leitch said it “may well be” the case that Glasgow stays in level three for longer than a week as he urged people in the city to take tests for the virus.
From today in level two areas, up to six people from three households can socialise indoors in a private home or garden without physical distancing.
Physical contact such as hugs with loved ones will be allowed again, though the government says people should use their judgment around how often this takes place.