United led 2-0 at Old Trafford through Javier Hernandez and Wayne Rooney before a second-half comeback from the visitors secured them a replay at Stamford Bridge.
"We're disappointed, especially after the way we played in the first half," Ferdinand told the club's official website.
"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.
"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."
The winners of United's replay with Chelsea will take on Manchester City in the semi-finals.