Mikel Arteta's side played well for large periods but left empty-handed, leading Gabriel Jesus - a four-time Premier League winner with Manchester City - to underline the need to kill off opponents.
"The feeling is frustration because we play, we control the game and the first two goals we concede we were better than them, the opponent," the in-form frontman said. "And then we just concede.
"But now is the time to learn from it and improve. We are doing so well this season but there are still things to improve for everyone, as individuals and as a team.
"Everyone is together and we stick together until the end.
"We came to play against a strong opponent and it's always hard, it's the Premier League.
"So we are not happy because, in my opinion, we could win because we play so much better.
"But that's football, they have quality as well and then if you don't go there and kill, you are going to have a big problem - and that's what happened."
Arsenal, who are still top of the Premier League table after winning five of their six games, will turn their attention to Europe this midweek.
Arteta's men will travel away to FC Zurich as they kick off their Europa League campaign.