The 31-year-old's Arsenal career is effectively over after he was also left out of their Europa League squad.
Ozil responded furiously to the decision, accusing Arsenal of a lack of loyalty.
"Everybody is free to express their feelings," Arteta said in response to the German's comments.
"It was just a football decision and my conscience is very calm because I have been really fair with him.
My level of communication with him has been high, we know what to expect with each other.
"He has had the opportunities like everybody else. I'm sad that I had to leave three players out of this list but I tried to look everybody in the eye and be comfortable with it.
"With Mesut, I have this feeling because I have been very straight forward since I arrived at this club.
"It's nothing related to [Ozil's] behaviour. It's my decision."
Arteta added that he took responsibility for not getting the best out of Ozil.
"My job is to get the best out of every player to contribute to the team performance," Arteta said. "At the moment I feel that I have failed because I want the best possible Mesut for the team.
"In some moments I was able to get close to that but at the moment I haven't been able to do it.
"This is the reality and we have to face it. The best way is to talk things through face-to-face.
"I take full responsibility, I have to be the one getting the best out of the players."