Rangers believe the trouble in Manchester city centre which marred the UEFA Cup final involved many people with no known history of following the club.
Rampaging fans were described as a "disgrace" who could have jeopardised England's bid to host the 2018 football World Cup, Gordon Brown warned on Thursday.
The Prime Minister condemned the supporters involved in violent clashes with police on Wednesday night - and said public drinking laws would also be reviewed.
Hundreds of fans turned violent when a big screen showing the match in the city's Piccadilly Gardens failed to work just before kick-off.
Fifteen officers were injured, as well as a police dog, and 42 arrests were made as hundreds of riot police and supporters fought running battles. One Zenit St Petersburg fan was stabbed but his injuries were not life-threatening.
Rangers chief executive Martin Bain returned to Glasgow on Thursday, and reflected on Wednesday's events.
"Unfortunately a screen went down in the centre of Manchester without maybe a separate feed coming in as back-up, and it has obviously been the catalyst for some incident," Bain said.
"Those scenes obviously are dreadful and I've seen them myself and we have been informed ... that those scenes were caused by supporters that don't normally attach themselves to our support.
"Therefore we're extremely disappointed and we'll do everything we possibly can to help Manchester Police find out who those perpetrators are."
Rangers security chief Kenny Scott insisted the club would "take the appropriate action" against trouble-causers.
"The club and the authorities, we have to identify anybody that was responsible for any of these acts of violence," Scott said on Sky Sports News.
"The club will take the appropriate action. The difficulty is of course that many of these people will have no association with Rangers Football Club and that exacerbates our difficulties in dealing appropriately with the situation which occurred in Manchester last night."
Scott stressed that plans to accommodate visiting supporters in Manchester city centre on the day of the game had been extensive.
"I don't think there's an awful lot more that could have been done," he said.
"We saw yesterday afternoon great scenes in the city of Manchester.
"The city absorbed the numbers that were there, despite the fact they exceeded the numbers which were expected.
"But unfortunately the catalyst for the disorder last night was the breaking down of the screen and though by no means do we condone the behaviour of the supporters who became involved in violence, particularly when police officers were injured and we particularly abhor that type of brehaviour, we still have got to reflect back on the fact that in the stadium the atmosphere was fantastic.
"We had positive comments from UEFA about the sporting behaviour of our supporters.
"In the city centre, if there were 120,000 people or so in the city centre, 200 or so according to police estimates and the estimates of the city of Manchester authorities, let down this club."
Scotland's First Minister Alex Salmond called for a wide-ranging inquiry into the clashes, and denounced the behaviour of "a small minority of fans" as "completely unacceptable".
He was speaking at First Minister's Questions where Labour leader Wendy Alexander called for an inquiry by Greater Manchester Police, Manchester City Council, Glasgow City Council, Strathclyde Police, and Rangers security.
Mr Salmond told MSPs: "The council have announced an inquiry this morning.
"I understand that initially at least it's quite limited in its scope, looking in particular to the circumstances of the equipment breakdown.
"I would think that the inquiry should be wider in its scope - there are a number of other aspects to inquire into."
He went on: "Certainly we will give full co-operation on all the matters under our responsibility to such an inquiry."
The match commander, Assistant Chief Constable Justine Curran, said the response of her officers was "appropriate".
She said: "It was challenging and we were stretched. Our officers did come under a degree of violent attacks. I am happy we responded appropriately. We could not let those minor disturbances affect the day for everybody.
"I am satisfied our reaction was appropriate. I watched the scenes in Piccadilly Gardens from the control room. I saw officers chased down a street by a baying mob of around 200 people. We had to do something."
The screen that failed was one of eight mounted in the city to accommodate more than 100,000 ticketless fans who travelled to Manchester.
Council leader Sir Richard Leese said the screen went blank 15 minutes before the 7.45pm kick-off but had been working throughout the day.
Around 11,000 fans were transported by shuttle bus to an alternative screen set up rapidly at the Velodrome near the City of Manchester of Stadium - but a group of supporters stayed and vented their fury at the police.
Sir Richard said: "We are clearly disappointed that a great night was soured by a number of small people.
"We had an unprecedented number of people come to Manchester, between 100,000 and 150,0000 people. It is the biggest movement of that size for an event of this nature.
"For most of the day and in most parts of the city we had a carnival atmosphere. Most people were good humoured who were a credit to their city.
"Whether it was the big screen going down or a problem with alcohol the behaviour of this small minority of yobs was not acceptable.
"If you are going to put the blame on anyone then it has to be on these people."
A relaxed attitude to fans' drinking in the street - normally outlawed - was adopted as supporters consumed alcohol from breakfast onwards.
Sir Richard added: "Do you really think we were going to stop 100,000-plus Glaswegians wanting to have a drink? It was not possible.
"Trying to enforce that would have created a public order problem."
