A protest outside Celtic Park that left three police officers with minor injuries is under investigation.
Fans gathered outside the stadium on Sunday calling for Hoops boss Neil Lennon to be sacked after the 2-0 Betfred Cup defeat to Ross County.
Dozens of officers and police vehicles formed a barrier as club staff left the ground.
No arrests were made and the three injured officers did not require medical attention.
The Parkhead club said in a later statement that some players were left "shaken" after being targeted by missiles while footage showed some fans kicking down and throwing barriers.
Chief Superintendent Mark Sutherland criticised the action, which came while restrictions are in place to stop the spread of coronavirus.
The divisional commander for Greater Glasgow said: "It was utterly disgraceful to see the violent scenes at Celtic Park on Sunday evening.
"Three of our officers suffered injuries, albeit minor, as a result of the behaviour which took place.
"Abuse and assault is not simply part of the job for police officers and staff and will not be tolerated. The Chief Constable has made it clear that this is completely unacceptable and he has committed to reducing the impact of violence and improving the safety of officers and staff.
"We have now launched an investigation to identify those who were involved in the disorder and violence towards police officers, players and officials.
"My message is clear, you won't get away with it, don't think just because you weren't arrested last night does not mean you escaped. If you are identified as being involved, you will be arrested.
"I would appeal to anyone who has any information that will assist this investigation to contact us through 101. Alternatively Crimestoppers can be contacted on 0800 555 111, where anonymity can be maintained."
It was Celtic's first defeat in 36 domestic cup ties and it left them with two wins out of 10 as they sit 11 points behind Rangers at the top of the Premiership with two games in hand.
Celtic are out of the Europa League with two group games remaining but they have the chance to complete a unprecedented quadruple domestic treble when they take on Hearts at Hampden Park on December 20.
Sky Sports pundit and co-commentator Andy Walker, who had two spells at Celtic, was disgusted about what took place outside Parkhead and insisted Lennon, deserves better.
He told Sky Sports Scotland: "I thought they were shocking. I thought it was disgusting and I've got to say I don't recognise those people as Celtic supporters."
Celtic confirmed that they will also be launching an investigation and part of the statement read: "For players and a management team, who have given so much in recent years and have delivered 11 consecutive trophies, to require an escort from Celtic Park while being targeted with missiles is simply unacceptable.
"While we understand that only a small number of people were involved in this behaviour, some of the actions this evening, which have obviously left our own players shaken, cannot be condoned in any way."
Questioned on the actions of fans at the stadium, First Minister Nicola Sturgeon said: "I don't care if you're a Celtic fan, a Rangers fan, Ayr United fan, no fan of football at all, anybody who attacks police officers is doing wrong and that is pretty despicable and I would say that across the board regardless of football or any other sporting affiliation."
She told the Scottish Government's daily coronavirus briefing: "We have advice against gatherings and every day I stand up here and say avoid crowded places.
"We have a limit on people coming together outside of six people from two households so it stands to reason any group of people that are gathering together in a crowd are putting themselves and others at risk.
"Whether it's football fans, rugby fans, any other kind of sport fans or just people in general please don't do it because right now in the middle of this pandemic it is a risky thing to do that puts you and other people at risk."
