Failure to qualify for the Champions League would cause Mesut Ozil and Alexis Sanchez to leave Arsenal, making the club also-rans for years, according to Paul Merson.
Merson also believes under-pressure manager Arsene Wenger "looks lost" in his role for the first time since taking charge over 20 years ago.
Arsenal are on the brink of crashing out of the Champions League at the last 16 stage for a seventh straight season having lost the first leg 5-1 to Bayern Munich at the Allianz Arena.
The fourth-placed Gunners also face a fight to return to the competition, with Liverpool and Manchester United close behind them in the Premier League table.
If Arsenal fail to make the top four, Merson predicts it would take his former club years to recover.
"If they don't finish in the top four this season, they will just be an also-ran club for a few years," he said to Sky Sports.
"Sanchez will go and I don't see Ozil staying there. They have a lot of players who have been there a long time.
"If they don't finish in the top four I don't see a world-class player going to play for Arsenal next season.
"If that doesn't happen, how are they going to get in the top four next season? Man City will buy again, Man United will buy again, Chelsea will buy again.
"Maybe Tottenham won't because of their new stadium but Liverpool will buy again. All of a sudden Arsenal get left behind."
Merson thinks Wenger is as vulnerable as he has ever been at Arsenal, but wants the players to take their fair share of the blame.
He continued: "I know it's been same old, same old for the last three or four years, but the other night [at Bayern] was the first time I have seen him look lost.
"Even in the press conference, he went in with the thought that he was in trouble. That is the first time I have really seen him like that. Usually he is quite confident and he will get out of it by saying the right words.
"Sometimes you have to draw a line, though. He takes all the stick and I'm one of those people that is probably on his back as much as anybody else.
"But these players are letting him down. He puts a team out and puts a lot of faith in these players who have been there for a long time - not like a year or two - these players have been at the club four, five and six years. Some even longer.
"They are not performing. They are letting him down and they keep on getting away with it."
27. Juni 2017
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|Stats amazing - Can marvels at Liverpool newcomer Salah|
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|FIFA response expected after Bild reveal Qatar World Cup report ´leak´|
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|Wall wants to see George in a Wizards jersey|
|Kaino: No intention to injure Murray|
|Germany v Mexico: Werner´s eyes on the prize as El Tri aim to start on time|
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|Australian cricketers preparing for unemployment – ACA president Dyer|
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|Nicklaus: Tiger Woods will have a hard time returning to golf|
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|Woods won´t be present for Quicken Loans National|
|Montella hopeful Donnarumma will stay at Milan|
26. Juni 2017
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|Bolt reminds rivals: I´m the fastest man in the world|
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|Home hope Watson ousts Eastbourne champion Cibulkova|
|Anything Drogba can do - Hazard invests in new NASL franchise|
|Lyon to keep Lacazette unless replacement bought, says president Aulas|
|Milan goalkeeper Donnarumma apologises for social media ´uproar´|
|Lyon snap up €10m Chelsea forward Traore|
|Green, Leonard & Gobert lead NBA All-Defensive First Team|
|Van Aanholt excited to learn new ideas from Palace boss De Boer|
|Pospisil sets up Djokovic Eastbourne clash|
|FIFA referees chief praises VAR but sees work to be done|
|You´re a wizard, Hummels: Bayern defender celebrates Harry Potter anniversary|
|Kolarov keen on Lazio return|
|Fiorentina put up for sale by Della Valle family|
|Russian World Cup chief labels doping claims ´made-up news´|
|Djokovic to retain Agassi for Wimbledon|
|Like father, like son: Germain hoping to write his own ´beautiful´ Marseille story|
|He made me - Lue would hire Iverson as a coach|
|Giro crash a Tour de France factor for Thomas|
|New Nantes coach Ranieri wants to ´forget´ Leicester|
|Watford new boy Hughes: Premier League too hard to turn down|
|Confederations Cup Social Diary: No rest for Ronaldo, Trapp still smiling and FIFA honours Marc-Vivi|
|Cavendish confirmed for Tour de France after glandular fever|
|Parish surprised by Allardyce´s Palace exit but excited by De Boer arrival|
|New Edinburgh deal for Lion Dell|
|No stepping stone: De Boer hopes to see out three-year Crystal Palace deal|
|Dutch courage needed? De Boer follows likes of Van Gaal & Koeman to Premier League|
|Kvitova pulls out of Eastbourne|
|Frank de Boer appointed new Palace boss|
|I´m in love with Italy - Former AC Milan star Pato open to Inter switch|
|Portugal v Chile: Pizzi ready for tough challenge as champions of Europe and South America clash|