The Premier League giants finished second in the top flight in the last two seasons.
While they were the closest challengers to Manchester City, they have no trophies since winning the FA Cup in 2020.
"I hope that will happen this season because they have to win something to keep the confidence of the players and the vision of the club,” Petit told football london.
"It's important if you want to keep the same ambitions, if you want the players to follow you every single game, you need to win something at the end of the season.
“If you asked this question to Arteta, he would tell you the same answer. Football, what is it? It's winning games, winning titles. And at the moment, after two, three, three years of amazing work, you need to win something.
“If I am a player at Arsenal and I've been playing for years over there and I saw the improvements of the team, as well individually, but at the end we never win anything...
“They won an FA Cup, but they need to reach more important targets; Premier League or Champions League. I'm not sure that the Champions League is the right season. But for the Premier League, I think they have something to say about it, definitely.”