The France World Cup winner has called for manager Mikel Arteta to hand a new player the armband despite the north London club's huge 3-1 win over table-topping Liverpool.
The victory took Arsenal to within two points of the league leaders and sees them level on points with Man City.
And the Frenchman hailed England international Declan Rice for his role at the heart of the midfield in that success.
Speaking to Compare.bet, Petit said: "Arsenal won the game because of the midfield.
"It was the key to the performance and they dominated the midfield physically, technically and tactically.
Read More On Arsenal
Thomas Frank gives honest answer on Ivan Toney's future which Arsenal fans will love
Ronaldinho, Henry and Ozil among names lined up for star-studded over-35 World Cup
"Jorginho and Rice were both absolutely brilliant."
Focusing on Rice, the former Premier League champion made it clear that he would prefer the ex-West Ham star to skipper the side ahead of Odegaard.
Naming the defensive midfielder as one of Arsenal's two best players alongside Bukayo Saka, Petit argued: "He should be Arsenal captain for me.
He continued: "He has such a brilliant character and he is a leader.
Most read in Football
Mourinho 'hands back Roma gift' and 'leaves nine-word message' for players after sacking
Chelsea fans send Silva's wife same message after apology for Pochettino comment
Meet the ball boy starring with Harry Kane, who could be a Euro wildcard and upset Alonso
Thomas Frank gives honest answer on Ivan Toney's future which Arsenal fans will love
"He has something different to the rest of the players and is so influential in big games."
Petit was less complimentary about current Arsenal skipper Martin Odegaard, who has drawn criticism recently for over-celebrating the Gunners' victory over Liverpool in the eyes of some.
The Norway international took a picture of club photographer Stuart Macfarlane on the pitch at full-time, and Petit labelled Odegaard's post-match antics 'strange'.
Jamie Carragher not impressed by wholesome moment between Martin Odegaard and Arsenal photographer
He then urged the group of players to not let the result go to their heads, observing: "You've just won a game, it's just three points. Calm down.
"You have to be careful. There's still 15 games to go and they were acting like they won the league."
Despite this, the fan-favourite was thrilled with the final score, praising the atmosphere as 'electric', which he attributed to the impact of the club's 'great manager'.
Petit was adamant that north London outfit, "Have to make sure Arteta stays," as the Gunners boss continues to be linked with a move elsewhere.