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"I think it would be a real mistake for what was a very very small minority of Rangers fans to say that their behaviour can be excused by a technical problem with a screen. If we are going to put a finger of blame anywhere it has to be with those fans having to take responsibility for their own behaviour."
The city council leader added that plans for the city to celebrate Manchester United's Champions League final appearance next week against Chelsea by putting on a similar event would now be cancelled because it would place unfair pressure on local people.
"It is an appropriate response to what happened last night," he said, adding that "any business or resident of the city centre" would agree.
Justine Curran, assistant chief constable of Greater Manchester Police, added: "A minority of thugs have overshadowed what should have been a great occasion."
She added: "I’ve watched them commit damage, assault my officers and I’m really sickened and disappointed. I saw officers chased up the street by a baying mob of 200 people. I saw an officer tripped and then stamped on by the crowd."
UEFA, European football's governing body, is investigating the violence. It was not yet clear whether the club could be punished for the behaviour of its supporters.
William Gaillard, the body's communications director, said police and the city had done a "fantastic" job in hosting the fans, a minority of whose behaviour had been "reprehensible".
"I can’t believe that any other city would have done anything better. Of course we are very disappointed with the behaviour of a small minority especially after the city had done everything it could to accommodate everyone’s needs and were rewarded by injured policemen and hundreds of tons of rubbish," he said.
Speaking at his monthly press conference, Mr Brown said the Home Secretary was discussing the matter with police in Manchester, and said the incident should not be allowed to damage the country's bid to host the 2018 football World Cup.
"It was a minority but it was completely unacceptable and for that to happen in a public place where the Manchester authorities had made available the facilities for people to enjoy the match," he said. "They have good reason, both the police and the authorities, to be very angry about what happened."
The Prime Minister said that the Home Secretary would explore with police how better to implement powers to stop people drinking in public in such situations. Adding that fans without tickets should in future think twice about attending a city, he said: "If you want to come to a city where you do not have a ticket for a match, you need to think twice about that."
Rangers' chief executive Mr Bain initially issued a statement this morning condemning the behaviour of "a small minority" of fans who caused trouble. However, he later admitted: "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 that the club would "take the appropriate action" against trouble-causers.
Alex Salmond, Scotland's First Minister, called for a wide-ranging inquiry into the clashes, and denounced the behaviour of "a small minority of fans" as "completely unacceptable".
Labour leader Wendy Alexander called for an inquiry by Greater Manchester Police, Manchester City Council, Glasgow City Council, Strathclyde Police, and Rangers security.
Rangers abandoned plans for a bus tour through Glasgow this afternoon following the death from cancer of Tommy Burns, a former Celtic F.C. legend.
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