Two police officers were “seriously injured” and 14 arrests were made during trouble in Glasgow after Celtic’s Premiership title win against Hearts.
Bottles and other missiles were thrown at officers as around 3,000 Hoops fans gathered in the Trongate area of the city after Saturday’s play-off.
Assistant Chief Constable Mark Sutherland said he was “disgusted and frustrated” by the violence shown towards officers.
He said Celtic FC needed to “step forward” to ensure there was no repeat of the disorder next year. The club has been contacted for comment.
Police Scotland said there were 10 arrests in the Trongate and four arrests at Celtic Park – with more expected in the coming days as CCTV footage is reviewed. A further four people were arrested in Edinburgh.
After Celtic’s 3-1 win over Heart of Midlothian to take their fifth successive Premiership title, fans gathered in the Trongate as they have done in previous years.
Initially the mood was lively with green flares let off and fans drinking but by early evening it had turned uglier.
Police officers who were assisting paramedics attending a medical emergency were pelted with bottles, and riot police were then used to disperse the crowd.
Sutherland said one officer was left with facial injuries while the other had been left with bruising to his body after being struck by bottles.
“First and foremost, I’m so grateful that only two officers have suffered serious injury,” he told BBC Scotland News.
“But when you see the footage and you see the incoming bottles and missiles being rained on our officers, I’m so grateful and we are very fortunate that only two officers have been injured on this occasion.”
By Sunday morning the rubbish strewn streets had been largely cleared up and traffic lights which were damaged by fans climbing on them were being repaired.
As a precautionary measure glass had already been removed from bus shelters ahead of Saturday’s title play-off.
Police Scotland had been critical of Celtic ahead of the game, saying that despite talks on the issue, the club had “failed” to bring forward a plan for fans to celebrate safely in the event of victory.
“Celtic must step forward into this space with the authorities, with the broader partnership and ensure that this isn’t happening again next year,” said Sutherland.
Glasgow City Council said the majority of fans had celebrated in the right way and complied with a request to stay away from Trongate.
“However, the behaviour of some people in the aftermath of yesterday’s match was, quite frankly, an embarrassment,” it added in a statement.
“They let down the city, their club and their fellow fans.”
At the end of Saturday’s game, the Glasgow side’s fans had also spilled onto the pitch as the third goal went into the net, with some reports that Hearts players were confronted by Celtic supporters.
Sutherland said the force was working with Hearts to establish what had happened and would be “carrying out an inquiry and reviewing CCTV to understand if any player has been assaulted or any other fan has been assaulted”.
The match, which was approaching the end of the indicated eight minutes of added time, did not restart after the pitch invasion.
The Hearts players and staff made a hasty exit from the ground, with some players still in their match kit on the team bus as they headed back to Edinburgh.
In a statement Hearts has condemned the “menacing and threatening atmosphere inside the stadium”.
“Hearts’ entire staff had no alternative but to leave immediately, without undertaking post-match media duties,” it said.
“The pitch invasion caused a chaotic end and nobody seemed to know whether or not the match had been brought to a finish.”
The SPFL condemned the pitch invasion but said that prior to awarding the trophy it was informed by the referee that the match had concluded, and had not been abandoned.
In a statement it said it would wait to assess the referee and match delegate’s report before making a decision about any potential punishment.
BBC Scotland understand the league body also intends to speak to the Scottish government about finding new ways to tackle the issue of pitch invasions.
In England and Wales it has been a criminal offence to enter the field of play since 1991.
The SFA are already investigating after on-field disorder following a cup match between Rangers and Celtic in March.