Ferguson's side were three goals to the good against ten-man City at the Etihad Stadium, only for goals from Aleksandar Kolarov and Sergio Aguero to give the home side a fighting chance of forcing a replay.
United managed to hold firm in the dying moments but Ferguson was still disappointed.
"I think we made them better than we were. Probably at 3-0 up we thought we were through, but we took our foot off the pedal," Ferguson told ITV Sport.
"They went into defensive formation, which you have to give them credit for, hoping that we made mistakes.
"It was a careless performance, we should have been home and dry."
United have not lifted the FA Cup since 2004.