Robin van Persie put the Red Devils ahead in the 19th minute with his 21st goal of the campaign before Nemanja Vidic managed to divert Patrice Evra's header into the back of the net ten minutes into the second half.
Liverpool winter signing Daniel Sturridge got one back for his team prior to the hour-mark before United held out for a win which sees them remain seven points clear at the top of the table and Ferguson was happy with the performance.
"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."