The Gunners led the league table by more than 200 days this season but a poor run of form has opened the door to Manchester City, who can now wrap up a fifth league crown in six years with victory over Chelsea this weekend.
Wright has spoken of his pride at Arsenal's title push, which few predicted would happen at the beginning of the season, but warned that his former team face a far tougher test next season.
"Obviously the initial reaction is one of massive disappointment, but I am so proud of this Arsenal team," Wright said on his podcast. "I haven’t got a problem with outsiders saying we bottled it, because they know we haven’t. You only have to look at the facts – the age of the team, the inexperience, the injuries.
"Arsenal flew close to the sun this season and they deserved to be flying at that height. But Manchester City are sensational.
"Looking ahead, the slight worry I have for Arsenal is that Mauricio Pochettino is heading to Chelsea so they’re coming. They have an excellent squad. I don’t know what’s going to happen with Manchester United but you know they aren’t going to sleep for too long.
"Liverpool are going to be making the signings they need to get them back to where they want to be. You look at those sides plus Man City and Arsenal – and even Newcastle – they’re all coming now and that’s exciting.
"If Man City can win five titles in six years and they keep winning, it’s tough because teams know they need at least 90 points to compete. Liverpool showed us it can be done but look at what it did to them.
"What we all need to be worried about is a situation where Man City just win it at a canter because while Liverpool and now Arsenal have given it a good go, they’re still doing it City. People mock the French and German leagues but the Premier League, if we’re not careful, is on that path.
"The only thing stopping that is teams like Liverpool and Arsenal standing up, that’s why we need Chelsea, Liverpool and Man United back and Newcastle coming up too."