Scotland's Deputy First Minister spoke out against the scenes on Saturday, which led to five police officers being injured and 28 arrests, with officers saying many more will follow.
Thousands of fans defied Covid-19 warnings against large gatherings and massed in George Square to celebrate Rangers winning their first Scottish Premiership championship since 2011.
Images showed George Square strewn with hundreds of broken bottles, plastic bags and spent flares after flag-draped fans had been seen attacking each other and launching traffic cones, plastic bollards and other missiles at lines of riot gear-clad police officers.
Mr Swinney told the BBC's Good Morning Scotland: "Every exhortation was given by Police Scotland, the Scottish Government and Rangers Football Club for fans not to assemble.
"But unfortunately 15,000 people did so and they started off behaving peacefully and then they descended into thuggish behaviour in George Square.
"I'm limited as to what I can say this morning because there's an ongoing police investigation but the conduct on Saturday was absolutely reprehensible.
"There was absolutely no need for them to gather, absolutely no need whatsoever, and the warnings were given very clearly ... and then some of them went on to behave in a loutish and thuggish fashion in George Square – devastating property, circulating and expressing vile anti-Catholic bigotry in the centre of the city of Glasgow.
"Police officers were assaulted on Saturday, which is completely unacceptable and obviously that will be a matter which is pursued vigorously by Police Scotland and so it should be and there'll be various actions taken to address the behaviour and the conduct of the fans on Saturday."
Calum Steele, general secretary of the Scottish Police Federation (SPF), tweeted images on Sunday of some of the injuries sustained by officers, including broken bones and lost teeth.
He described the scenes as "horrific", also telling the BBC programme: "There are almost no polite words left to describe how bad the events [were] in Glasgow at the weekend – and indeed the wider west of Scotland.
"Many of the officers who are quite long in the tooth have probably quite rightly described it as some of the worst violence that they've experienced in over 20 years of police service.
"People being critical of the police, that's nothing new, and those that don't have an appreciation and understanding as to what's involved in the policing tactics are rarely shy in holding back their points of view.
"The notion that the very limited resources of the police service would go into a crowd of that size to enforce the dispersal without any consideration of the inevitable consequences of such action I think shows just how narrow the thinking of those that are critical of the police in those circumstances are.
Police Scotland Assistant Chief Constable Gary Richie also said: "If we're going to actually take preventative action it's as going to actually cause a huge amount of disruption to the city, because we will need to close off roads and access points and you need to think about where the crowd, who would still be intent on coming, where they would be displaced to."