Dimitar Berbatov scored twice to give United the lead but Steven Gerrard scored a penalty and a free-kick to level the scores.
However, the Bulgarian 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 an overhead kick which went in off the bar, and 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."