Ozil reacted to being taken off against Manchester City last weekend by kicking his gloves away angrily.
And after the match, Freddie Ljungberg said: “How he reacts is up to him and I’ll deal with it.
“We’ll see what it means for the future but of course we want players to behave the right way.”
Arsenal revealed Ozil was dealing with a foot injury that would be assessed, ahead of the clash with Everton, and when the atrting line up was announced, Ozil was not included in the squad.
When asked about Ozil’s absence Ljungberg said: “Mesut has something on his foot but we have things happening there so he wouldn’t have been in the squad anyway after what happened in the last game.”
When asked about Ljungberg’s comments, Keown gave a damning assessment of Ozil’s commitment.
“I’m not convinced,” he said on BT Sport.
“What I will say is Freddie Ljungberg has managed with a great deal of dignity and a great deal of calm in difficult circumstances.
“Ozil is one of those problems that Arteta must manage that.
“He went off the pitch against City and he wasn’t best pleased. He didn’t look particularly injured on that occasion.
“He probably just took himself out of it because he thinks Freddie wouldn’t play him.
“Smith Rowe comes in today and I like the fact he wants to go with youth.”
The match is Ljungberg’s last before Mikel Arteta takes over on Sunday and the Swede called on his players to show their quality for the new manager.