Arteta was shown a straight red card six minutes from time after appearing to catch his Spanish compatriot in the face with his elbow.
"I don't blame Cesc for what happened, but the referee got it wrong," Arteta said.
"He should have seen that it was just a coming together of players and nothing intentional, it was not a red card.
"The referee has to know the players and the way I play - I always use my arms. I never try to hurt anybody or kick someone because I am not a player like that.
"I can't understand it. He didn't whistle when the challenge was done but after three seconds when he saw Fabregas on the floor I knew he was going to send me off."
Fabregas felt Arteta deserved the red card for the offence.
"He is my friend but this is football. It just happened," noted Fabregas.
"The one thing I am sure about is that he put his elbow in my face and that is a red card."