The Premier League champions were second best all over the pitch as Manchester City dominated at Stamford Bridge.
Kevin de Bruyne got the only goal of the game as Chelsea struggled to create clear-cut chances.
And after the match, Conte suggested Chelsea’s exertions in midweek against Atletico Madrid had left the players drained.
He said: “It was a tough game but we know very well that Manchester City are a big team and it’s very difficult to play this type of game.
“I think that we gave everything today and I am happy with the commitment and desire from all my players. They had the will to fight against a very strong team.
“In this type of game you need time to recover, if you are tired it is not simple to go box to box.
“Today we created chances but we didn’t take them. Manchester City had chances and they took them.”