Rome prefect Achille Serra said the fans were stabbed in either the groin or backside during clashes with Roma supporters. He also said that at least three of the 18 fans reported injured were Italian.
Serra insisted that police had acted properly and that the clashes inside the stadium "lasted no longer than two minutes."
"On both sides there is a category of violent imbeciles who use knives," Serra said at a news conference Thursday.
Steven Fitzsimons, who was stabbed in the groin, told AP Television News that he and his friends were ambushed by Roma fans outside the stadium and that there were no police around.
"I got hit in the back of the head, I stumbled to the floor," he said "When I got up, we were surrounded by Roma fans all with knives. They just attacked us, stabbed us and that was basically it."
Fitzsimons, who was taken to the San Giacomo hospital, said the police still hadn't interviewed him.
Meanwhile, three United fans who were arrested by Italian police in a separate clash during Wednesday's quarterfinal first leg at the Stadio Olimpico will face fast-tracked trials, the British Embassy in Italy said. It was not immediately clear what charges the three Britons will face.
A British Home Office official, Vernon Coaker, told BBC radio: "The scenes that we saw on our television screens were extremely concerning. We need some explanation of what actually took place and the police response to it."
British Officials said its government is gathering evidence from embassy staff and witnesses.
In Rome, the British embassy said that it had supplied a report on the match to the Home Office, and that Manchester police were working "in partnership" with Italian police.
"As the Home Office has already stated, we are concerned by the scenes in Rome last night," the embassy said in a statement.
Shortly before halftime, police in riot gear clashed with some of United's 4,500 fans. Police hit fans with batons as opposing fans taunted and threw objects at each other across the partition separating the rival sections. At least one fan was seen lying in the stands with blood all over his face.
Roma won 2-1. The second leg in Manchester is on Tuesday.
UEFA expects to announce later Thursday whether it will open any disciplinary hearings.
"We are waiting to look over the information from the reports of the delegate, the match official and the safety and security officer before deciding whether to open a disciplinary hearing, or what the charges might be and the dates," UEFA spokesman Robert Faulkner said.
"Hopefully, we'll be able to confirm whether we will open a disciplinary hearing and give some kind of indication of what direction it will take and what the potential charges might be. Whether both clubs or one club will be involved, the owner who is in charge of the security, that kind of thing," he added.
Tensions were high after United issued a pre-game warning on its Web site to fans traveling to Rome. It told fans to avoid certain areas of the city and not to use the train system because "there is a real danger of being attacked by the 'Ultra' fans of AS Roma." Rome officials said it would inflame tensions.
Manchester United said Thursday in a statement that it would look into the police clashes with fans.
"There were clearly some very disturbing scenes in the stadium on Wednesday night," the club said on its Web site. "Until we have had chance to discuss the situation with the British Embassy in Rome and the Italian authorities and to understand the cause, it would be inappropriate to comment."
Former referee Anders Frisk, who attended the match, told Britain's Sky Sports News that Italian police overreacted.
"What caused it was something that had been thrown," he said. "The Italian police reacted very, very aggressively toward one or two incidents."
In 2004, the Swedish referee was hit in the head by an object thrown by a fan during a Champions League match between AS Roma and Dynamo Kiev in Rome. He was taken to the hospital with a bleeding forehead, and Dynamo was later awarded a forfeit victory.
"It was very bad for me to be back at the Olympic Stadium and witness what was once again not good for football," he said.