The Gunners finished in fifth place in the Premier League table last term to miss out on a place in the Champions League this season.
Arsenal manager Arsene Wenger signed Lyon striker Alexandre Lacazette in a club-record £52m deal last month, while Bosnian defender Sead Kolasinac completed a free transfer from Bundesliga side Schalke 04.
The north London side won the Community Shield last weekend thanks to a penalty shootout victory over Premier League champions Chelsea to offer encouragement ahead of the new season.
But Arsenal made an unconvincing start to the new Premier League season following a 4-3 victory over Leicester City at the Emirates Stadium on Friday night.
The home side were badly exposed by the pace of Jamie Vardy as Arsenal were forced to come from behind twice to secure three points despite Lacazette giving the hosts a second-minute lead.
Former Manchester United defender Neville raised some familiar concerns about Arsenal following the seven-goal thriller in north London.
“It is the question that we ask year in, year out,” Neville told Sky Sports.
“The spine and conceding goals. That weakness was evident tonight, they were vulnerable. I’m sure they’ll be really concerned about how vulnerable they looked.
“They’ve got to correct that because they’re fantastic going forwards.”
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