City always looked the more likely to score with the game poised at 1-0, but Cech believes that a point was there for the taking if his teammates took more of a gamble early in the second half.
"We feel that we could have got something from the game," he 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 have just two victories in their last nine opening weekend Premier League games.