Arteta credited Norwich for their performance at Carrow Road but insisted that his side cannot afford to lose games that they enter as favourites.
He told the club's official website: "We're really down because we expected to win the game, they raised their game, they made it very difficult for us.
"I think we controlled the game, mostly, for 90 minutes. But you go a goal down, you start getting anxious, the goal doesn't come, it makes it really hard.
"For the amount of ball we had in the game, we should have done more. We are down because we know how good we are and how good we can be."
Arsene Wenger's side have the chance to respond quickly on Wednesday when they host in-form Schalke in the Champions League.