The Gunners went down to a 3-1 loss at the Emirates despite Manchester United going down to 10 men when Paul Pogba was sent off.
But Petit saw enough from his old side to suggest they are destined to finish in the Champions League spots.
The Frenchman has even likened the current stars to Arsene Wenger’s Invincibles, for who Petit was a star for.
He told Paddy Power: “The Gunners showed huge passion on Saturday and they need to hold onto that mentality moving forward. The way they played with desire and offensive flair reminded me of how we used to play.
“In the second half, I saw a great Arsenal team on the pitch – they showed fantastic character and personality.
“Arsenal will definitely make the top four if they keep that level of performance up.
“They are probably out of the title picture, but anything can happen – in 1998, we were 12 points behind in February and pulled that back.
“If City lose at United and then Spurs, it could be wide open again.”
Sanchez and Ozil couldn’t find a way past David De Gea but their form has improved of late.
Petit hopes they both stay but he reckons their better displays could be down to the transfer window opening soon.
He said: “Alexis Sanchez and Mesut Ozil are coming back to the way they should be playing for Arsene Wenger.
“It’s great news for Arsenal that they’ve returned to form, but is that just because the transfer window is around the corner?
“Who knows if they still want to leave? I really hope they remain at the club but, if they do, they need to show the same commitment to help Arsenal to a Champions League spot.