After the dismissal of Unai Emery, Ljungberg was placed in caretaker charge.
But Petit told Paddy Power News: "We need a new manager to come in and change the mentality of the dressing room. Bring the team spirit with anger and what it means to wear the Arsenal shirt. To put the players on the pitch with confidence. Because things can change.
"Freddie (Ljungberg) knows the team very well, inside the dressing room, but I don't know what exactly he can do as a manger, because this is his first time.
"Also, while all the mess was going on with the club, we didn't hear anything from him. I'd have preferred that he'd communicated at that time. So I'm not convinced he can be in charge for the long term.
"I'm very impressed with what Nuno is doing at Wolves. Their progression has been perfect. I really like him as a manager, he has the right mentality for the club, and the results – after a slow start to the season – have been excellent at Wolves."