The Frenchman has questioned if the 24-year-old had the determination to win a regular starting berth at the Santiago Bernabeu following the recruitment of similar players
The Germany international was unveiled at Arsenal on Thursday, following his €47 million move on deadline day.
The Spanish giants boosted their attacking options over the summer with the high-profile acquisitions of Isco and Gareth Bale respectively, and Zidane has claimed that the Gunners new-boy lacked the stomach to compete for his selection in the starting line-up.
"Ozil decided to leave," he told the club's official channel. "He is a good player who has given us so much so we wish him well.
"There are players who have responded with strength and will to fight for a place, but not everyone reacted the same.
"[Angel] Di Maria responded well and wanted to fight."
The Blancos travel to newly-promoted Villarreal in the Primera Liga on Saturday where €100 million recruit Bale could be handed his debut.