A number of supporters clashed with riot police after a big screen in Manchester broke down. Officers later confirmed 42 people had been arrested.
The Rangers team had been scheduled to take part in a parade on their return to Glasgow, but club officials have decided to cancel the event.
They said that in the light of the death of former Celtic player and manager Tommy Burns, it was “wholly inappropriate” to have a public procession through Glasgow.
The club would like to extend its sincere condolences to the family of Tommy Burns at this very sad time.”
Burns had been undergoing treatment in both Glasgow and France in recent weeks after being diagnosed in March.
In preparation for the Uefa Cup clash, Manchester City Council had set up three special fan zones with big screens for tens of thousands of ticketless fans to watch the match.
While screens in Albert Square and Cathedral Gardens did show the game, the one in Piccadilly Gardens failed about 15 minutes before kick-off.
Throughout Wednesday the atmosphere had been friendly for the clash between Rangers and Zenit St Petersburg.
Paramedics attacked
However, violence broke out at about 1930 BST after the screen in Piccadilly Gardens failed.
The broken big screen was pelted with bottles, as were riot police who moved in to try to quell the trouble.
Police and council officials blamed a “minority” of fans.
Rangers fans blamed the local council’s “shambolic” organisation, but another said the behaviour of his fellow supporters left him “ashamed to be a Scotsman”.
The general secretary of the Rangers Supporters Association, John MacMillan, said he was disappointed with the behaviour of some fans.
He added: “There is no excuse for it to be honest. From what I saw before the game there was no need for attacking paramedics and the police, it is indefensible.”
A spokesperson for Greater Manchester Police said: “We would like to stress that the vast majority of supporters have behaved impeccably and came to Manchester clearly intent on enjoying the carnival atmosphere.
“It is believed that more than 100,000 supporters travelled to Manchester without tickets, almost all of whom came with the intention of enjoying the occasion.”
There were dejected scenes in Glasgow, where 25,000 fans had watched the match on giant scenes at the club’s home ground, Ibrox Stadium.
Strathclyde Police confirmed that they made 17 arrests in Glasgow on Wednesday evening.