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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 to better 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 without tickets, 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 issued a statement this morning condemning the behaviour of "a small minority" of fans who caused trouble. Some of the club's supporters had blamed the scenes on "shambolic" organisation by the city but others were reported as saying that the behaviour had let the reputation of their city down.
Martin Bain, the club's chief executive, said: "The club has had discussions with Greater Manchester Police and Manchester City Council in view of incidents in the city last night.
"The police and council praised the behaviour of the overwhelming majority of Rangers fans and estimates suggest there could have been around 200,000 in the city yesterday.
"There was a tremendous atmosphere all around the city and the vast majority deserved credit for the way they behaved. The police and council have identified the failure of a big screen in the city as a key point in the evening.
"We are deeply disappointed that a small minority soured what was great carnival atmosphere and this is a view shared by our fans who travelled in unprecedented numbers to Manchester.
"We would like to thank everyone in Manchester who made such a great effort to welcome our fans to the city yesterday."
Rangers announced that the club had abandoned plans for a bus tour through Glasgow this afternoon following the death from cancer of Tommy Burns, a former Glasgow Celtic legend.
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