The German playmaker headed straight for the dressing room after the final whistle at the Etihad Stadium while his team-mates went over to applaud travelling supporters.
His actions appeared to incur the wrath of defender Per Mertesacker, who remonstrated with his fellow German as he left the field.
Now Ozil, who has had a huge influence since his deadline-day arrival from Real Madrid, accepts he should not have done as he did.
In a statement on his website, www.mesutoezil.com, the 25-year-old said: "Sorry I didn't thank the fans at the end of the game!
"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 defeat at City saw the Gunners' lead at the top of the Barclays Premier League cut to two points.