The result led to manager Arsene Wenger questioning whether or not his side would finish in the Champions League spots, and Gray believes that Arsenal will have overachieved if they do.
"In the 22 games Arsenal have played so far they're not one of the top four sides in this country," Gray told talkSPORT. "Arsenal sit where their performances suggest they should be, which is around fifth or sixth.
"Arsenal are not better than Tottenham, who are a more rounded side. They're not better than Chelsea, who are playing well at times but look nervous at their own ground, and they're certainly not as good as the two Manchester clubs.
"Arsenal are competitive, they showed that against Chelsea, but they can't take on teams like they did when they had Patrick Vieira, Emmanuel Petit, Tony Adams and Steve Bould. They haven't got an iron spine."
Arsenal host West Ham United in the Premier League on Wednesday.