Substitute Ryan Babel's mishit shot 13 minutes from time finally ended a United run of five successive league victories against Liverpool.

Carlos Tevez's early opener was cancelled out by a Wes Brown own goal, and Liverpool dominated the second half against a United side who finished with 10 men after Nemanja Vidic was dismissed for a second yellow card offence.

"It's great," Carragher told Sky Sport.

"It's been too long and it's not just the three points. It's also the belief and confidence it gives us, because we've beaten the best team in Europe. It gives us the belief that we can beat anyone in the league.

"We hope we can now push on for the rest of the season. It should spur us on, because we've not been playing too well up to now. That is the best we've played today.

"It also gives us a bit of breathing space between us and United, and top is where a club like Liverpool should be."

Liverpool boss Rafael Benitez was delighted with the way his side fought back from the early Tevez strike.

"It was good for the confidence of the players," he said.

"At half-time we were talking about having confidence and determination going forwards - and in the second half we were the best team.

"We showed quality and character to come back, and the understanding of (Robbie) Keane and (Dirk) Kuyt was very good. Their pressing was really important for the rest of the team."

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Disappointed United boss Sir Alex Ferguson admitted his side failed to handle Liverpool's combative approach.

"You don't expect that from Manchester United," he told Sky Sports.

"When we have a bad day we usually still get something from the game

"Overall, they were the better team today. Liverpool produced a performance of tackling, hassling and getting about us.

"The source of our defeat was not coping with the hassling and the tackling. You have to give them credit for that - but at the end of the day, we should cope.

"We started excellently, and it was a wonderful ball from Berbatov for the goal. But I can't really take anything from the game, apart from Rio Ferdinand's performance."

Reflecting on the end of a run of five successive league wins over Liverpool, Ferguson mused: "The difficulty of holding a record like that is that it gives the other team a big incentive every time they play you."

The United boss, asked about Vidic's dismissal, retorted: "Carragher was making those challenges all day long, and no fouls were given.

"We had several bookings and a red card. Is that a reflection of Man United being a dirty team? I don't think so. I think the crowd plays a part."

England midfielder Michael Carrick did not emerge for the second half after being injured in a 50-50 first-half challenge with Yossi Benayoun, but Ferguson reported: "I don't think anything is broken."