Dimitar Berbatov scored twice to give United the lead but Steven Gerrard scored a penalty and a free-kick to level the scores. However, Berbatov completed his hat-trick to give United a 3-2 win, which Ferguson thought was the least his team deserved.
"From thinking to myself, 'It's going to be 10', we ended up at 2-2," he said. "It was a travesty of a scoreline then - but a great result at the end.
"They (Liverpool) didn't offer anything and depended on decisions from the linesman to get back in the game. Edwin van der Sar had no saves to make, Paul Scholes controlled the midfield and we looked dangerous up front with Dimitar and Nani - I couldn't see us losing the game."
Berbatov's second goal was the pick of the scoring, an overhead kick which went in off the bar, and after the Bulgarian had become the first United player to score a hat-trick against Liverpool in more than 60 years, Ferguson added on Sky Sports: "It was unexpected, a surprise attempt. Not many of those go in the net but fortunately it did this time.
"There was a lot of criticism of him (Berbatov) last season from the media - it happens when we buy someone for a lot of money, that's the way of the world - but this season he has started off in the right fashion. He was good in pre-season and on tour and has carried it on. There has never been any doubt about the quality of the man."
Ferguson revealed Ryan Giggs and Rio Ferdinand have been suffering from a sickness bug, adding: "Ryan was ill at half-time and was feeling really queasy. Rio was the same last night, so we hope it's not going to spread."
Liverpool boss Roy Hodgson said: "I thought our second half performance was good and we deserved to get back in the game. I think we were a bit unlucky to go two down when we did - and of course to concede late on was tough.
"We're disappointed but otherwise I thought we made a really good effort in the second half to get back in the game. Had we had a little bit more composure at the end maybe we'd have seen the game out.
"In the first half I don't think the front players received that many balls they could deal with, more because of good defending than anything else, but then the game opened up and there was more excitement for the fans in the second half."
Fernando Torres won both the penalty and free-kick which Gerrard scored from, and Hodgson added: "Fernando is still a player who needs more games, time and training - but we'll get a lot of tremendous use out of him for the rest of the season."