The Scot accepted some of his side's defending - their Achilles heel all season - had been "erratic and desperate" in the second half but ultimately it did not matter.
"I would have taken that score before the game," said the United boss. "Winning against Liverpool is important. It doesn't matter where you are in the league."
Robin van Persie's 21st of the season put United ahead in the 19th minute and Nemanja Vidic doubled the lead just after the break - inadvertently deflecting in Patrice Evra's header.
Substitute Daniel Sturridge pulled one back, his second in as many games after joining from Chelsea for £12million, when he fired home after goalkeeper David de Gea had parried Steven Gerrard's shot, setting up a tense finish for the Barclays Premier League leaders, but they ground out victory.
Ferguson added: "The first-half performance, and until we scored the second goal, was absolutely brilliant. It was as good a performance as we have had for a long time and we should have been three or four up but when they got their goal they got inspired by it.
"Their supporters got going and it was hard work after that. I am just glad we won the match. I haven't seen the (Liverpool) goal again but it looked a bit soft; once again the keeper has parried one out and nobody is following in the rebound.
"It lifted them. Some of our defending after that was a bit erratic and even desperate at times."
Liverpool manager Brendan Rodgers admitted a limp performance in the first 45 minutes had cost his side.
"I felt we were too tentative in the first half - but you can understand with young players playing here," he said. "There wasn't much in the first half but any chances they had were through us giving the ball away. I said before we went out that when you play a rival - and this rivalry is massive - you need courage and you need to have belief."
- Sports & Recreation
- Nemanja Vidic