The club issued a statement on the scenes which followed a 2-0 defeat to Ross County in the Scottish League Cup.
Hundreds of fans defied strict lockdown rules to congregate outside the stadium after their team crashed to a 2-0 loss.
Some were seen charging at security fences and clashing with security staff as players departed the stadium in a convoy of cars.
Two police officers sustained minor injuries, and there were no arrests - but the gathering, and the behaviour, sparked widespread criticism.
Humza Yousaf, Scotland’s Justice Minister, described the scenes as “utterly disgraceful” and said the violent conduct of a minority of fans towards police was “shameful.”
He tweeted: “Utterly disgraceful scenes outside of Celtic Park from a minority of fans tonight with violence aimed towards Police. Officers have been front & centre keeping us safe during this pandemic. To treat them this way at any time is shameful, to do it during these times is a disgrace.”
Now, Celtic FC have also said the scenes could not be condoned.
In a statement, the club said: “While we sincerely share the huge disappointment of all Celtic supporters, there can be no excuse for some of the violent scenes at Celtic Park this evening.”
Pledging a full investigation, it continued: “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.”
The ugly scenes started late afternoon as a large number of fans gathered outside the stadium and vented their wrath at manager Neil Lennon and the team following the cup defeat.
Superintendent Stevie Dolan, Greater Glasgow Division said no arrests were made, but two officers sustained minor injuries.
He said: “"An appropriate policing response was carried out and the group has now dispersed. “We strongly condemn these actions and remind fans that enforcement options remain at our disposal.
"The Scottish Government regulations are clear that protests are prohibited in areas under level four restrictions and we would urge people to find alternative ways to protest to prevent the spread of coronavirus.
"Disorder of any sort will not be tolerated and appropriate action will be taken where any offences are identified."
Veteran TV commentator David Tanner was among many media forced to run the gauntlet of the angry crowd when leaving the stadium.
He tweeted; “Disturbing scenes at Celtic Park. Tensions are naturally high but this is the wrong approach. Sorry. Spare a thought for the Police Scotland officers on the ground dealing with this.
"As an aside, Glasgow is currently tier 4 lockdown...Football-wise, this is end of Empire stuff.”
Fellow commentator and TV pundit, ex-Celtic legend Chris Sutton, said: “The people protesting outside Celtic Park can’t call themselves Celtic fans. True Celtic fans wouldn’t be singing despicable songs about a man who has given the club the service Neil Lennon has. They are a disgrace. Self entitled a**es.”