Rafa Benitez's side found itself two goals down minutes into the second half and was unable to produce a comeback despite Demba Ba pulling one back late on.
The Belgium international says the Blues were "frightened" of Roberto Mancini's men in the opening period and that ultimately cost the club a place in the final against Wigan.
"We were frightened of City in the first half," he told The Sun. "We showed them too much respect and paid the price. Maybe we might have deserved a different fate, but we started the game badly.
"We played the final 40 minutes, but that is not enough to beat City. We had chances, and we believed we could do something, but their keeper made some good saves."
Chelsea faces Fulham in the Premier League on Wednesday hoping to claw itself back into pole position in the race for the Champions League.