Five police officers were injured and 28 people arrested as crowds were dispersed due to "rising disorder.”
Several people were assaulted, property was damaged, and flares were thrown at Police Scotland officers after Rangers supporters marched from Ibrox stadium to George Square.
First Minister Nicola Sturgeon was among several high-profile politicians to condemn the actions of the club’s supporters, tweeting that would be an understatement to suggest she was “utterly disgusted” by those fans who “rampaged” through the city.
Now, the club has issued a four paragraph statement on its website addressing the disorder.
It said: “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 FC.
"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.”
The statement did not address what, if any, action the club intends to take against those supporters found to be involved in the violence. The Scotsman has asked Rangers it is actively looking to identify and ban any such fans.
The club’s statement said it was grateful to Scottish Government officials, Glasgow City Council, and Police Scotland for what it described as “constructive engagement” in the lead up to Saturday’s game, which saw Rangers presented with its first Scottish Premiership title in a decade.
It added: “We worked closely with the authorities for two weeks before Saturday’s march to ensure a consistency of message.”
The club said it will continue to engage with authorities as required.
It comes as Rod Petrie, president of the Scottish FA (SFA), described the scenes in Glasgow as an “abomination.”
He said: “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.”
He added: “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.”
In a statement, the SPFL said: “The behaviour of many fans at Ibrox during and immediately after the game, and the subsequent major disorder in Glasgow city centre, was utterly shameful.“As the club themselves have said, this behaviour was unacceptable, and especially so given the repeated advance warnings regarding social distancing.”
It added that it supported the actions of the courts, the SFA, and the club in “dealing severely with those who have so badly let the game down.”