Arsene Wenger's side began their continental campaign in miserable fashion on Tuesday, falling to a comprehensive 2-0 defeat against Borussia Dortmund in Group D.
Arteta admits the scoreline flattered Arsenal, after an error-strewn performance, and insists they must up their performance level significantly to compete with the best in Europe.
"If you make the mistakes that we did, against top sides, we know that there is no chance to win the Champions League," the midfielder told reporters.
"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 next engagement is a Premier League clash away to in-form Aston Villa on Saturday.