Arsenal legend Tony Adams fears the team may have already peaked under Mikel Arteta.
Arsenal had looked like favourites to win the Premier League for much of the season before falling away in the final weeks of the campaign, with Manchester City going on to claim a third successive title instead.
Their capitulation in the league means Arsenal will end the campaign without a piece of major silverware for the third season in a row under Arteta.
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Arsenal are expected to back the Spaniard with significant transfer funds this summer to ensure this season's title challenge was not just a one-off.
But former Arsenal captain Adams, who won four league titles with the north London club, fears they may have missed their only opportunity to be crowned champions under Arteta.
Adams fears for Arsenal
Writing in his column for The Sun, Adams said: "I do fear that this could be as good as it gets for them.
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"Talk of Arsenal bottling the title race was nonsense because they played to their absolute maximum and came up just short of the best team in the world.
"No one expected them to finish so high but the downside to all that is where do they go from here?
"I hate to sound like a prophet of doom, but I do believe that a lot of this team has already peaked.
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"It was possibly the best season that many of them will ever have. I don't think they'll get to that level again.
"They're definitely not going to challenge Manchester City next season and without serious recruitment this summer it will be a struggle for them to finish runners-up again.
"City's B team is better than any other Premier League side and we know that Newcastle, Manchester United, Liverpool and Chelsea will all be much stronger next time out."
Arteta: We must be much better
Arteta has already warned his Arsenal side they cannot rest on their laurels and must be "much better" if they want to beat City next season.
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"We wanted to bring the club back to the Champions League. That was the main target," said Arteta.
"We didn't expect to finish where we are. I think it's the third best record in the club, with the history of the club, the most wins ever.
"It's a lot but it's still not enough to win it. We understand where the level is. If we want to be the real deal, we can't be happy with what we have, and we have to be next season much better."
Topics: Arsenal, Football, Mikel Arteta, Premier League