The Gunners were beaten for the first time in this season's competition on Tuesday as they went down 2-1 to the German outfit at the Emirates Stadium.
Arsene Wenger's side remain at the top of Group F after three matches, but they are now level on points with Dortmund and Napoli.
"I think we deserved better," Arteta told the club's official website.
"It was when we had control of the game and created the best chances when we just got caught on the counter-attack. That was disappointing.
"We're still capable of going through but we're really disappointed with the way we lost the game."
Arsenal return to Premier League action on Saturday when they make the trip to Crystal Palace.