Police officers were attacked after a big screen due to broadcast the game to 20,000 fans in Piccadilly Gardens failed before kick-off on Wednesday evening.
Fifteen officers were injured and a police dog injured a paw, while one Zenit St Petersburg fan was stabbed at the City of Manchester Stadium.
Eleven Rangers fans, all men, were charged with various offences. Murray stressed that Rangers "deplore" the behaviour of the groups of supporters who tarnished the club's appearance in the showpiece match.
He announced: "The club can confirm today that we are already taking steps to deal with the people who have appeared in court and have been convicted of involvement in the disturbances on Wednesday, and they can consider themselves banned from any further recognised involvement with the club.
"The club will process bans with immediate effect." Murray added: "Since Wednesday night the club has worked non-stop analysing the disturbances which occurred in Manchester.
"On behalf of the club I am grateful for the recognition from Manchester City Council, Greater Manchester Police and many Mancunians that the overwhelming majority of our supporters behaved well during their visit to the city and were a credit to the club.
"We deplore the actions of a small minority who were involved in the disturbances and support the severest action taken against them.
"We are continuing to liaise with the police and city councils in Manchester and Glasgow and will be assessing all relevant information over the coming days, including numerous reports given to us by our supporters, before making any further statement."