Cech believes the Gunners made lots of mistake during the second half of the encounter, adding that they lacked invention to find the killer pass against the Premier League champions.
“We feel that we could have got something from the game,” Cech told BBC Sport.
“In the second half, we forced them to make mistakes and we had some opportunities. Unfortunately, we lacked invention to find the killer pass.
“When you play against a team of City’s quality and confidence it is always going to be difficult.
“Inevitably, you can make a few mistakes. It was a shame we couldn’t finish off our counter-attacks and overall we’re disappointed with the defeat.”
Arsenal will face Chelsea in their next EPL game on Saturday.