Ozil was hooked during Sunday's 2-2 draw with Crystal Palace.
Working as a pundit for Sky Sports, Souness said: "There was 15 or 20 minutes at most where they were the best but the rest of the game I felt was Palace's.
"I still think they are much of the same to what we've seen the last few years. And I think it's typified by Ozil. To be fair, Ozil showed a great deal of passion when he was subbed today [and] that's the most I've ever seen him show in a game of football. It's no good showing petulance like that.
"You're the captain, when you're on the pitch show courage to get on the ball when you're not dominating, show real passion… and maybe if you're not built for it but make an attempt to get into a few challenges and win the ball back for your team but he doesn't do that.
"I'm sorry to harp on about him but a man with that much talent should influence games like that."