The Red Devils boosted their title hopes with the narrow victory at Old Trafford, with goals from Robin van Persie and Nemanja Vidic securing the points.
Although his side had to defend late on following a Daniel Sturridge effort, the Scot was delighted with their display:
“I would have taken that score before the game,” he is quoted by Sky Sports.
“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.”
Fergie went on to praise his team for digging deep in the second-half to grind out an important three points:
“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.
“The name of the game is winning. There are moments where you have to defend. Today was one of them.”
Van Persie rounded off a fine team move to sweep home with his left foot after 19 minutes, giving the home side the lead.
Vidic then added a fortuitous second, deflecting a header from Patrice Evra past Pepe Reina.
Liverpool pulled one back after 57 minutes, as Sturridge reacted well to a David de Gea parry.