City, who made eight changes from the side that beat Dortmund, failed to break down a resolute Chelsea defence and created only a few decent chances in what was an off-colour performance at Wembley.
Worryingly, Kevin De Bruyne limped off minutes into the second period with an ankle knock.
Hakim Ziyech grabbed the winner on 55 minutes.
The first-half had few thrills and even less chances.
Chelsea started brighter and had an early goal ruled out and Ben Chilwell should have scored when Reece James picked him out at the far post and he volleyed wide.
City created little of note with Chelsea defending in numbers and looking comfortable in what was a slow-paced first 45.
On 55 minutes, Chelsea went ahead when City were caught on the counter-attack with Timo Werner's break down the left ending with a low cross for Hakim Ziyech to turn home.
Three minutes later Zack Steffen made an excellent stop as Ziyech broke clear only to his low shot saved by the American.
City improved in the latter stages, but Kepa was rarely tested in what was ultimately a disappointing afternoon at Wembley.
WHAT IT MEANS...
City's FA Cup adventure is over, as are the hopes of a domestic clean sweep of trophies.
The Carabao Cup final is next weekend and City will hope to erase the disappointment of this Wembley loss quickly.
It's back to Premier League action on Wednesday with a trip to Villa Park to face Dean Smith's Aston Villa.
Kick-off is 20:15 (UK).
“They played a good first 15, 20 minutes and we struggled a little bit.
“For the last ten minutes of the first half we were better - we didn't create much but we were there.
“In the last minutes with Phil and Gundogan on, we created more. Congratulations to Chelsea.
“They are strong, well organised with seven players in the middle, experienced.
“You need actions of quality. We were there. In general, the guys didn't give up. It was a tight game.
“We didn't find the key players in the pockets. We didn't create much, but in the last minutes it was much better.
“I am delighted with what we have done so far. The number of games we have played - we haven't had a midweek in an eternity.
“Now it’s Aston Villa - we need ten points and we need the first three. And then final of Carabao Cup and then semi-final versus PSG.”
Chelsea:: Kepa, Azpilicueta, Chilwell, Jorginho, James, Kante, Mount (Pulisic 70), Rudiger, Silva (Zouma 88), Werner (Havertz 79), Ziyech (Emerson 79)
Subs: Caballero, Alonso, Gilmour, Hudson-Odoi, Giroud.
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