The summer signing from Real Madrid netted his side's first goal of the night at the Emirates Stadium as the Gunners earned a 2-0 victory in Group F.
"It's a really nice feeling - especially to score at home," Ozil told the club's official website. "You could see that the fans really supported us up until the last minute.
"What was important was that we won the game. Of course I'm pleased to have scored, especially at home. It was my way of thanking the fans."
Tuesday's result saw Arsenal move to the top of Group F, three points clear of second-placed Napoli.