Brentford put up a fight at the Etihad Stadium, where goals from Riyad Mahrez and Kevin De Bruyne gave the hosts victory.
Mahrez opened the scoring with a first-half penalty after Mads Roerslav had brought down Raheem Sterling.
And De Bruyne doubled the lead following a terrible mistake by David Raya.
Keeper Raya, recently back from injury, gave the ball straight to Sterling and saved the England star’s shot but was powerless to stop De Bruyne’s easy follow-up.
Brentford were without the injured Ivan Toney and Vitaly Janelt and always faced a tough task against the runaway Premier League leaders.
The Bees can take heart from their performance but have now lost six matches in a row in all competitions and are just six points above the relegation zone.