The defeat has seen them move into a three-way tie at the top of Group F.
Henrikh Mkhitaryan fired the visitors ahead but Olivier Giroud grabbed an equaliser before Robert Lewandowski scored in the final 10 minutes to move Dortmund level with the Gunners and Napoli on six points.
And while Arteta admits Arsene Wenger's men are in a tough group, he does not believe that Tuesday night's defeat will derail their campaign.
"It's going to be tough," he told ITV1. "We knew that it was probably the toughest group in the Champions League, we don't think any different now.
"We are still capable of going through but we are disappointed to lose the game.
"I think we played some really good stuff and we were unlucky to concede the goal when I thought we were playing the better football."
He added: "We did the hardest bit to score just before half-time and I thought that we had control of the game and were creating the better chances, we just got caught on the counter attack
"I think we gave the ball away at the edge of the box and we know they are a very good side on the counter attack. I think we kept them really quiet but obviously they got that chance and they scored."
England midfielder Jack Wilshere caused some concern when he pulled up with an ankle injury towards the end of the first half when he chased a through ball into the Dortmund penalty area.
Wilshere, though, felt he would be okay for the weekend's Premier League game at Crystal Palace.
He said: "I jarred it when I was going through (on goal).
"My ankle stopped and my body went over it and I jarred it a little bit.
"For five or 10 minutes it was painful, then I ran it off, but it made sense to put ice on it.
"I've done that before, even before I had surgery. It is just one of those things.
"Obviously I will have treatment tomorrow because it is still a bit swollen, but I should be all right for the weekend."