Ozil made just his third appearance of the season as Arsenal were knocked out of the Carabao Cup by Premier League leaders Liverpool.
The chaotic match finished 5-5 after 90 minutes and Liverpool held their nerve to convert all five penalties and book their place in the quarter-finals of the competition.
Ozil produced an impressive performance at Anfield, playing an influential role in two of Arsenal’s five goals before his surprising 65th-minute substitution.
Emery has hinted at Ozil’s inclusion against Wolves in their upcoming Premier League game and Carragher insists the German playmaker has to start more games.
He told Sky Sports: “I’m not Ozil’s biggest fan you cannot tell me he is not good enough to get into this Arsenal team as this isn’t a great Arsenal team.
“The criticism with Ozil is whether he can take them to the Premier League title or the Champions League, but at the moment Arsenal are going for the top four.
“So he’s got to be in the team or best XI. No one is doing anything consistent for Arsenal at the moment, not just Ozil.
“If you look at the front three, I am sure they would love to have Ozil feeding them.
“Arsenal are in a position where so many players are not at the top of their game that they almost have to put up with what Ozil doesn’t do.”
On the thrilling cup tie, Carragher added: “Some of those young players especially on the Liverpool side, that’s the greatest night of their life.
“They’re starting their careers, who knows where it’ll go, but I’d be surprised if there are more exciting games that they play in their career than tonight.
“I thought the young players on both sides were in some ways better than the senior ones, the senior ones made a lot of mistakes that led to goals.”