Arteta was dismissed for an alleged elbow on the Arsenal youngster.
Replays revealed it was a harsh decision against Arteta, who now faces a three game ban.
But Fabregas insists referee Martin Atkinson was right to display the red card to his friend.
He said: "He is my friend but this is football. It just happened, the same with Nicklas. Everyone can have their opinion but the one thing I am sure about is that he put his elbow in my face and that is a red card."