The Gunners dropped points for the first time in this season's competition as they were beaten 2-1 at the Emirates Stadium.
Despite remaining at the top of Group F, Arsenal are now level on points with Dortmund and Napoli with three games left.
"It's going to be tough [to qualify], we knew it was probably the toughest group in the Champions League. We don't think any differently now," Arteta told the club's official website.
"We're still capable of going through but we're really disappointed with the way we lost the game."
Arsenal continue their Premier League campaign on Saturday when they face Crystal Palace at Selhurst Park.