Arsene Wenger's side began their continental campaign in miserable fashion on Tuesday, falling to a 2-0 defeat at Dortmund in Group D.
That the scoreline ultimately flattered Arsenal resonated with Arteta, who called on his side to turn things around.
He said: "If you make the mistakes that we did, against top sides, we know that there is no chance to win the Champions League.
"We encouraged them to do that by giving the ball away so many times in very difficult positions. They exploit the spaces very well and they put us under pressure.
"I am bitterly disappointed. I am very disappointed because we knew their strengths, what we had to avoid and what we did was encourage them to play their game.
"We have to react. We have to analyse what we have done wrong and try to improve. In four days, we have another game. That is the best thing, another game to try to react and improve."
Arsenal's first chance to respond to the Signal Iduna Park thrashing comes in the form of Saturday's trip to early high-flyers in the Premier League Aston Villa.
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