Arsenal agreed a 12.5 percent reduction in wages with their players and coaching staff on Monday but Ozil was one of three players who reportedly refused to agree to the terms.
Ozil is Arsenal’s highest paid player with a weekly wage of £350,000.
"The fact the highest-paid player and possibly the biggest name at Arsenal has not gone with the rest of his team-mates and stuck together [is bad]," Carragher told The Football Show on Sky Sports News.
"Even if I was in Ozil's position and I did not agree with that, I think the fact the rest of the team, your manager and people at the club have decided to be as one and make this decision, you have to go with it as a team.
"Football is a team game, it's not an individual sport, and for someone like Ozil in that situation I think he's got to go with what the rest of the players are doing. It's a massive PR own goal.
"I'm not going to have a go at Mesut Ozil for the wages he's earned. If you want to have a go at Mesut Ozil for the wages he's got, blame the people who gave him the contract. We're all in every walk of life trying to earn as much money as we possibly can.
"But when a situation like this comes in and you're together as a team in a dressing room, I think the highest-paid member and the biggest name in that dressing room should be the one who almost sets the example really."
