The Germany international took to social media on Saturday to respond to his critics, suggesting that he has been wrongly targeted in the past by the Gunners' vocal former players.
Wright, who is among those to have questioned Ozil's displays in the past, believes that the 28-year-old must extend his stay at the Emirates Stadium beyond next summer if his remarks are to be taken seriously.
"Sign a contract if you feel that strongly about people criticising the team because you're somebody who is integral to Arsenal's success," he told BBC Sport.
"You're not signing a deal and you're probably going to continue to hide behind the fact that [Alexis] Sanchez is the one that everybody's going to say, 'Is he going to go?'. If you feel that strongly, why haven't you signed yet?"
"[Former players] all feel the same because we're all passionate and we all love the club. What are we supposed to say? That they're unbelievable, in the boardroom, the boss, and the way they're playing? Because they're not. I can't understand it."
Ozil and Sanchez are two of seven Arsenal players whose contracts are due to expire next summer.