The Reds were forced to hang on in the closing stages, despite taking a two-goal advantage through Robin van Persie and Nemanja Vidic. But Daniel Sturridge pulled one back to spark a late revival by the visitors.
"All in all, it was an engrossing game, as we expected in a Manchester United-Liverpool match," he told MUTV. "It's full of emotion, intensity and it's great to win. It was a magnificent performance in the first half, as well as we've played for a long time. It was hard work after they scored, to be honest with you, and I'm just glad we won the match.
"I think winning is important – it doesn't matter what league position we are in. I've said many times, it's a fantastic challenge between the two most successful teams in the country. I think those three points today are very, very important ones."
The manager felt Shinji Kagawa deserved a penalty when he appeared to be pushed into Pepe Reina during a scramble just before half time and paid tribute to Danny Welbeck for a tireless display.
"[The first goal] was a great build-up, terrific football, and a great finish by Robin but we should have been three or four up," added the boss. "I thought we should have had a penalty when Shinji was brought down.
"Danny was fantastic. I thought he gave them a real hard day of it, the two centre-backs. He and Robin, particularly in the first half, gave them a very difficult time. The reason Danny played