Rangers say "a small minority of people" have "besmirched the good name" of the club following disorder in Glasgow city centre.
Steven Gerrard and his side lifted the Scottish Premiership trophy on Saturday with fans marching from outside Ibrox.
Twenty-eight arrests were later made with Police Scotland stating more would follow the "disgraceful" scenes.
The Scottish FA has also released a statement describing incidents as an "abomination".
"We will continue to engage with authorities as required," Rangers said on their website.
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"We worked closely with the authorities for two weeks before Saturday's match to ensure a consistency of message.
"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 Football Club.
"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."
Following Rangers' win over Aberdeen and the trophy presentation, a large crowd, who were not allowed inside the stadium, marched into central Glasgow while the city remained in level three of Covid-19 restrictions, which prohibits large outdoor gatherings.
They made their way from Ibrox Stadium to George Square where flares were set off and missiles thrown. Police broke up the crowds after about five hours because of "rising disorder", with five officers assaulted.
Police Scotland have now established a dedicated inquiry team to investigate the trouble.
Detective Inspector Craig Warren said: "The public can be confident we are doing everything possible to identify those responsible for the violence and disorder. This will take time due to the numbers involved.
"We are reviewing CCTV, video and still images and I would appeal to anyone who may have captured incidents on their mobiles to please get in touch with us."
Earlier, Scottish FA president Rod Petrie commented: "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.
"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."
And a spokesperson for 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.
"We fully support the actions of the courts, the SFA and the club in dealing severely with those who have so badly let the game down."