The Reds, who knocked Manchester City out of the Carling Cup in midweek, claimed another notable scalp thanks to goals by Daniel Agger and Dirk Kuyt, with Park Ji-sung replying for the visitors.
Much was made in the build-up to the match about the responsibility of both players and fans to show restraint in the first meeting between the two sides since their stormy league encounter in October.
Patrice Evra, who was involved in an altercation with Liverpool's Luis Suarez in that match that subsequently resulted in an eight-match ban for the Uruguayan, was predictably booed by the Anfield support but in their conduct otherwise never crossed the line.
United more than kept home goalkeeper Jose Reina occupied during the 90 minutes, with Antonio Valencia in particular unfortunate to strike the post with a shot in the first half, and Ferguson admitted defeat was a bitter pill.
"I don't know how they lost it," he told ITV1.
"Just one breakaway, one bad break against you, and you can lose the game. It's a sudden-death situation and we've experienced it many times over the years.
"It was a bad goal [Kuyt's] because we didn't deserve that. But I'm pleased with my players, they performed very well, dominated the game, didn't deserve to be beaten at all in fact.
"We were the better team, but that's FA Cup football I'm afraid."