The Red Devils cemented their lead at the summit of the Premier League with goals from Robin van Persie and Nemanja Vidic either side of half-time.
Brendan Rodgers' visitors were galvanised by the introduction of recent arrival Daniel Sturridge, who halved the lead with a close-range goal that set up a nervy final half-hour - but Ferguson's men stood firm to take the points.
"I would have taken that score before the game," said the United boss. "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. 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 Ferguson had claimed their arch-rivals were so far behind United he did not know where they were in the league but, after extending the gap between themselves and eighth-placed Liverpool to 24 points, he changed his tune slightly.
"Winning against Liverpool is important. It doesn't matter where you are in the league," he added. "Manchester United-Liverpool games are fantastic challenges.
"They are the two most successful teams in the country. Today hopefully those three points will be very important."
Despite the victory Ferguson could not resist a dig at referee Howard Webb for not awarding United a penalty when Shinji Kagawa went down in a challenge with Andre Wisdom in an incident which saw the Japan international collide and injure goalkeeper Jose Reina.
"We should have had a penalty when Shinji was brought down. Howard Webb wasn't going to give us that," said the United boss, who was more complimentary about Van Persie's strike.
"It was a great build-up, terrific football and a great finish."