Rangers bosses have also taken aim at their own supporters, claiming those involved have "besmirched" the club's name with the scenes of disorder in Glasgow.
Five police officers were injured and 28 arrests made as the illegal mass gathering in George Square got out of hand.
Officers say there will be "many more" arrests to follow.
And now furious Scottish Football Association president Rod Petrie has issued a stinging rebuke of those who indulged in fighting, public drunkenness and sectarian singing.
"The Scottish FA congratulates Rangers on winning the Scottish Premiership title," he said in a statement. "While the majority of the club's fan base will have celebrated this achievement safely and in line with Covid-19 guidelines across the country and beyond, the scenes witnessed in and around Glasgow's George Square have brought embarrassment to the national game.
"Scenes that require the First Minister, Justice Secretary, Police Scotland and the Scottish Police Federation to issue condemnatory statements, and images that dominated the news agenda throughout the weekend, represent an abomination not a celebration.
"Those responsible for sectarian singing, for vandalism and for inflicting physical damage may attach themselves to football but cannot be considered football fans. Police Scotland have made a number of arrests and more are expected to follow.
"Events on Saturday at George Square served only to depict our game in the poorest light and we condemn the behaviour in the strongest terms.
"We empathise with fans who have been deprived of attending matches throughout this pandemic. That, however, does not excuse the behaviour of those who brought chaos to the streets in the name of football this weekend."
Gers released a statement last week urging fans to stay away from Ibrox and the city centre as Steven Gerrard's team collected the Premiership trophy following their final match of the season against Aberdeen.
Manager Steven Gerrard also joined police and government officials in pleading with fans to abide by Covid rules.
But those warnings were ignored, with estimates of up to 15,000 people descending on Ibrox and the city centre.
"Winning our 55th league title in our 150th year was a historic day for Rangers Football Club," said the Ibrox outfit in a statement. "The support from millions of our fans across the world has been incredible.
"We are grateful to Scottish Government officials, Glasgow City Council and Police Scotland for the constructive engagement in the lead up to the weekend's game. We worked closely with the authorities for two weeks before Saturday's match to ensure a consistency of message.
"Sadly, a small minority of people behaved inappropriately and in a manner not reflective of our support.
"Some of the scenes were unacceptable and have besmirched the good name of Rangers Football Club. These so-called 'fans' should reflect upon the values and ethos of our club, and consider the damage this does to the reputation of the club.
"We will continue to engage with authorities as required."
First Minister Nicola Sturgeon branded the scenes " utterly unacceptable" on Sunday as she called on Rangers to "reflect on what more must be done to tackle this behaviour by fans".