The Gunners have collected back-to-back victories over West Ham and Cardiff after opening the season with successive defeats.
Unai Emery has managed to find a winning formula, but his side have been breached eight times in four games.
Petit believes it's those issues, which have carried over from Arsene Wenger’s time at the club, which will ultimately prove to be Arsenal’s undoing and undermine the efforts of their frontmen.
A man who tasted title glory with the Gunners in 1997-98 told RMC Sport: “Arsenal's defence is still a long way from the level needed to compete with the top four teams in the Premier League.
“We saw it again against Cardiff. It is a recurring problem, that dates back years with Arsenal.
“It has never been fixed, neither by Unai Emery, nor Arsene Wenger, nor the players out on the pitch.
“Pierre-Emerick Aubameyang and Alexandre Lacazette can score 40 to 50 Premier League goals a season between them if they are picked to start matches.
“But even with these two, Arsenal won't be able to finish in the top three if they don't sort out their defensive problems.”
Even those inside the Gunners camp have acknowledged that they remain leaky at the back.
Lacazette conceded after netting the winner in a 3-2 victory over Cardiff that there is still work to do.
He said: “We are learning a lot but the manager says we will concede goals.
"We just make mistakes because we are learning like children. So it is okay it is good. We will be better week after week."
Arsenal did make three defensive additions over the summer, with Stephan Lichtsteiner, Sokratis Papastathopoulos and Bernd Leno drafted in.
It is, however, taking time for the Gunners to adjust to Emery’s demands, with the likes of Petr Cech struggling to come to terms with a system which emphasises the need to play out from the back.