The Germany international headed to the Emirates Stadium on transfer deadline day in September for a £42.5 million fee.
He has since become a key part of Arsenal's squad, making 24 appearances this season - scoring five goals and assisting 10 more in that time.
Ozil's departure was seen as vital to make room for Gareth Bale's arrival at the Bernabeu, but Real have spent almost all of the season lagging behind Barcelona and Atletico Madrid in La Liga.
Sunday's win at Espanyol moved them to within three points of the table-topping pair, who remain deadlocked after a 0-0 draw at the Vicente Calderon on Saturday.
Another key departure from the Bernabeu over the close-season was Gonzalo Higuain, who moved to Napoli.
Ancelotti does not see Higuain's sale to be as damaging as Ozil's, though.
"I think we made a mistake when we gave him (Ozil) the possibility to leave the club," Ancelotti said.
"However, we have fantastic strikers and don't need a back-up after Higuain's departure."
Ancelotti's claims may dampen any hopes Arsenal have of loaning Real striker Alvaro Morata in January.
The 21-year-old is reportedly a target for Arsene Wenger, although Ancelotti is likely keen to keep his striking ranks well-stocked as they compete in La Liga, the Copa del Rey and UEFA Champions League.
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