The Reds were 2-0 up after just 11 minutes but ended the game hanging on and grateful for David De Gea, who made a brilliant late save to deny Juan Mata from close range.
Ferdinand, who was terrific for long periods in the heart of United's defence, was visibly frustrated during his post-match interview with MUTV, claiming Chelsea should never have been allowed back into the game.
"We're disappointed, especially after the way we played in the first half," he said. "We should have put the game out of sight. In the second half we gave them the impetus to go on and get back into the game.
"David made a great save at the end to keep us in the game and the tie. We should have finished the game off in the first half, though. Had we done that we wouldn't be talking about any saves at the end of the game.
"The frustrating thing is that the attacking play in the first half will get overshadowed now and nobody will talk about it. We'll probably talk more about how we finished the game, which wasn't on a good note.
"We were playing some great football but we were also careless at times. At this level, if you're careless you'll get punished. Today that was the case."
Indeed, Sir Alex told MUTV he thought United were "lucky" to still be in the FA Cup following Sunday's second-half performance. The boss believes last Tuesday's Champions League tie against Real Madrid took its toll on some of his players, who looked