The Sky Sports pundit believes that the Gunners' senior stars have been unable to withstand the pressure of competing with Manchester City for the Premier League title and Neville always had "doubts" about how they would cope.
Neville said: "Experienced players stay still, they stay calm, they settle everything down and make sure they get you through difficult moments. That is what I always doubted. The Arsenal spine has wobbled at the most difficult time. They were never capable in my mind of holding it together."
However, Neville thinks that Arsenal can learn from the experience if they recruit wisely in the transfer market.
He said: "But that is not to say they can't in the future. They can develop that experience, they can add a couple of players, Mikel Arteta is a young manager. So all is not lost here."
Neville pointed out that experienced Arsenal stars such as Thomas Partey and Granit Xhaka have struggled as Arsenal have frittered away points in recent weeks.
He explained: "City have put them under pressure but City were always going to squeeze them. That is what happens in every title race. You never win your first title easily. It may have happened but you just don't. It is a struggle. It is a massive struggle.
"You need vast experience to come through that and I always wondered whether Arsenal had that experience, I always doubted it. I always doubted their experience at the end to cope when the young players would feel the pressure.
"I think we have seen Gabriel, [Thomas] Partey, [Granit] Xhaka and a couple of others, their weakest time of the season. They have lost their form and the older players have not been able to settle the younger players who were inevitably always going to struggle in this moment through pressure.
"The experienced players have just not been quite there for them."