The Scot accepted some of his side's defending, which has been the weakness of the team all year, had been erratic in the second half, but admitted this was of little significance at the final whistle.
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 after inadvertently deflecting in a header from Patrice Evra.
Daniel Sturridge pulled one back after coming off the bench, netting his second in as many games since joining from Chelsea when he pounced after goalkeeper David de Gea had parried Steven Gerrard's shot, but the home side worked hard to hang onto their lead .
Sir Alex said: "I would have taken that score before the game. The first-half performance and until we scored the second goal, we were 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.
"The Liverpool goal looked a bit soft; the keeper has parried one out and nobody is following in for the rebound.
"It lifted them. Some of our defending after that was a bit erratic and even desperate at times.
"But we managed to get through it. The last three or four minutes they were shoving players into the box and there was some interchange play we had to deal with.
"The name of the game is winning. There are moments where you have to defend. Today was one of them."
Prior to the game Fergie had claimed his Anfield arch-rivals were so far behind his side that he did not know where they were in the league.
But after extending the gap between themselves and the eighth-placed Merseysiders to 24 points he slightly changed his tune.
He added: "Winning against Liverpool is important – it does not matter where you are in the league. Manchester United-Liverpool games are fantastic challenges.
"They are the two most successful teams in the country. Hopefully those three points will be very important."
Despite the victory, the Man United boss could not resist a dig at the man in the middle for not awarding a penalty when Shinji Kagawa went down in a challenge with Andre Wisdom in an incident which saw the Japan international collide and injure Jose Reina.
He said: "We should have had a penalty when Shinji was brought down. Howard Webb wasn't going to give us that."