Arsene Wenger's men suffered a 1-0 loss to Atletico at the Wanda Metropolitano on Thursday, beaten 2-1 on aggregate in the last four.
Ozil was unable to have an impact for the Premier League side, who had just one shot on target in the second leg.
Keown – who won three league titles at Arsenal and made more than 300 appearances for the club – was scathing in assessing the Germany international's display.
"That is not a proper performance. He's not giving everything. There's much more under the bonnet. Somebody else will find it," he said on BT Sport .
"Whether the new manager coming in can find it, I don't know, it's a big problem for the new manager because Wenger's invested an awful lot of money in this player and I'm not seeing a performance to go with it.
"He wasn't fit to wear the shirt for me tonight. I've seen this a lot this season and it needs to be said because it needs to be dug out because we expect better from him.
"He's a World Cup winner. These are crocodile tears I'm seeing from the player, he's not conning me."
Ozil signed a long-term deal with Arsenal in February after plenty of speculation over his future.
Wenger defended the former Real Madrid midfielder, saying Keown was off the mark.
"I don't agree with that," he said. "I think you will see that when you analyse his physical performance that he gave a lot tonight.
"It was a difficult game, physically very intense and I'm convinced Ozil should not be now vindicated by anybody because we didn't score.
"We had plenty of opportunities in the two games. We lose as a team.
"I don't agree with that, coming out now straight away. When you want to be listened to now you always have to be extreme."