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."
19. März 2018
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|Having Rabada in third Test massive - Elgar|
|Cavs coach Lue steps away from job due to health reasons|
|Debuchy disappointed to be left out of latest France squad|
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|Hamilton can become greatest F1 driver in history - Kovalainen|
|Sevilla coach Montella interested in Italy job|
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|I´ve had enough - Pietersen confirms retirement|
|UEFA charges Marseille and Lyon for Europa League trouble|
|Broad ready to do damage in New Zealand series|
|Injured Chiellini out of Italy squad|
|Toulon-bound Webb out for rest of season|
|Buffon cites Astori among reasons for Italy return|
|Welbeck faces no action over alleged dive against Milan|
|Charnley switches back to league to join Warrington|
|Barcelona? I´m staying with PSG, insists Marco Verratti|
|Bastian Schweinsteiger & Ana Ivanovic announce birth of son|
|The numbers behind Cristiano Ronaldo´s 50 hat-tricks|
|Woods relishing end to frustrating Augusta absence|
|Consistency the only thing stopping me from being the best, claims Depay|
|Guardiola second to none tactially, says Man City midfielder Gundogan|
|McIlroy: Bay Hill win a huge confidence boost for Masters|
|F1 2018 Pre-Season Report: Mercedes|
|F1 2018: The best Opta facts ahead of the new season|
|Liverpool captain Henderson ponders Salah and Suarez comparison|
|Messi worried by the uncertainty retirement brings|
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|Hunt handed ban and fine but cleared to return|
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|Guptill added to Black Caps squad|
|Thunder end Raptors´ streak, Davis stars|
|Stars goalie Bishop expected to miss at least two weeks|
|Messi desperate for World Cup success|
|Federer frustrated by Indian Wells final defeat|
|Del Potro: I can´t believe I won Indian Wells|
|Napoli causing Juventus problems as Sarri revels in crucial win|
|Balbirnie happy to boost Ireland chances|
|The better Ronaldo is, the better Madrid will be – Vazquez lauds four-goal hero|
|Ireland inspired by retired team-mates – Sexton|
|Indian Wells crown surreal for Osaka|
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|Salah ´unstoppable´ like Messi, says Watford boss Gracia|
|Demanding Mourinho is still special, insists Matic|
|Truex Jr sweeps stages and wins first race of 2018|
|Woods pleased with progress at Bay Hill|
|McIlroy cruises to victory at Bay Hill, where Tiger impresses|
|Dallas 3 Seattle Sounders 0: Dempsey sees red after VAR|
|Ronaldo ´from another galaxy´, says Zidane|
|Del Potro saves match points to stun Federer for Indian Wells title|
18. März 2018
|Eusebio Sack-ristan: Real Sociedad part company with head coach|
|Fassone ready for Gattuso talks after Milan resurgence|
|Napoli 1 Genoa 0: Albiol goal maintains pressure on Juve|
|Real Madrid 6 Girona 3: Four-goal Ronaldo continues hot streak with 50th career hat-trick|
|USA boss Sarachan calls up Weah for Paraguay friendly|
|Excellent Leipzig deserved Bayern win - Heynckes|
|Marquez will sleep easily after last-ditch Qatar move|
|Conte impressed by Morata´s return to scoring form|
|I lost the game myself - Simeone accepts responsibility for Atletico Madrid defeat|
|Borussia Dortmund to delay final Stoger decision - Zorc|
|Toulouse topple leaders Montpellier|
|Puel stands by Schmeichel after FA Cup blunder|
|Neymar could be back for Coupe de France final, says Silva|
|Valverde waits on Iniesta answer as Barcelona captain considers exit|
|Magnificent Osaka claims maiden title at Indian Wells|
|Villarreal 2 Atletico Madrid 1: Unal deals LaLiga title race blow for Simeone´s men|
|Leicester City 1 Chelsea 2 (aet): Pedro and Morata send Conte´s men through|
|RB Leipzig 2 Bayern Munich 1: Werner strike seals memorable triumph|
|Gattuso demands lift from out-of-favour Kalinic|
|Karthik hits final-ball six to win Nidahas Trophy|