The Gunners were unable to penetrate Kasper Schmeichel's goal despite having 11 shots in the first-half.
"I'm really disappointed, we had it in our hands in the first half and I don't know how the hell the goal was disallowed," Arteta told BBC Sport.
"They caught us with space at the back and in that moment we lost the game.
"It is difficult to create spaces with 10 men behind the ball, but we should have finished the game better. When it comes to those moments you can't give away chances at the back.
"We still had some moments after the goal but gave away too many free kicks. The effort that the boys put in, and the pressure the Leicester team put you under, it's not an easy thing to do but we have to improve."