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 for Chelsea after 55 minutes at Wembley.
Watch the best bits from the encounter via the video above.
You can watch full-match replays of every City game with a CITY+ subscription.