The Germany international refused to applaud the Gunners supporters at the end of the City defeat, but he has since said sorry for his behaviour at the Etihad Stadium
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However, Ozil said on his official Facebook account later in the day that he regretted his actions and only behaved in the manner that he did as he was disappointed with the loss.
"Sorry I didn't thank the fans at the end of the game," he wrote.
"You have been brilliant to me and I know you had travelled a long way and spent your money to support us.
"I was upset with the result and know I should have come to you to say 'thank you' and I know it is a big Arsenal tradition win, lose or draw."
The loss for the Gunners rounded off a disappointing week which also saw them drop points against Everton and lose to Napoli in the Champions League.
The victory for City means they are now just three points behind the Premier League leaders.