Ancelotti's men cruised to victory against the Basque side on Sunday, with Isco finding the net twice and Cristiano Ronaldo scoring his first goal of the season.
However, Ozil was forced to watch from the bench as Ancelotti omitted him from the starting XI.
Ozil also showed his frustration at being substituted during Monday's 1-0 over Granada as he stormed straight down the tunnel and reportedly spent the remainder of the match on the team bus.
Ancelotti accepted that the Germany international, who has been linked with both Arsenal and Manchester United in the transfer window, was displeased not to have featured against Bilbao, but insisted the decision was not related to a prospective transfer.
"It's normal Ozil is not happy now," he said.
"I don't like players who like staying on the bench. He is not happy, which is normal.
"It was a technical decision for lining up (Angel) Di Maria with more pace and intensity and that's it."
Real full-back Fabio Coentrao is another player whose future has been the subject of speculation, but Ancelotti is adamant the Portuguese will not be leaving the Bernabeu.
"Fabio Coentrao is staying," he added.
"I think everybody is happy although I understood he wanted to leave. I didn’t have the will of his leaving and I think everybody, the club, players are really glad of this decision."
On making it three wins out of three in La Liga this season with victory over Bilbao, Ancelotti added: "It was a good match.
"It is true we didn’t start with intensity but after 15 minutes the team started to do well with more pace. I think team are improving."
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.