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."
|Nailiko banned for Hibbard punch|
|Taylor gets two-game ban for Coleman challenge|
|Betting ban effectively forces me into retirement - Barton|
|ECB members approve new Twenty20 tournament|
|Gignac: I´d die before I signed for PSG|
|India miss Champions Trophy squad deadline|
|Barton banned for 18 months over betting breaches|
|Messi only plays well for Barcelona - Romario|
|England all-rounder Ansari announces shock retirement at 25|
|Bruno ordered to return to prison|
|Tomic injury hands Murray Barcelona walkover|
|Tigers land Bulldogs playmaker Reynolds|
|David Moyes charged by FA over reporter ´slap´ comment|
|West Ham involved in HMRC probe into suspected tax fraud in football|
|Widdop out for around six weeks|
|Ronaldo out of Real Madrid clash with Deportivo|
|Slater still has Australia future - Meninga|
|Champions League final in Monaco sights, says Glik|
|Serena pressed ´wrong button´ to reveal pregnancy|
|Vardy made right call in snubbing Arsenal - Shakespeare|
|Tigers score 19 runs, Turner leads Nats to big win|
|Drake to host first-ever NBA Awards show|
|Harden and Rockets advance past Westbrook´s Thunder, Spurs poised|
|James wants Real Madrid stay, says wife|
|Nationals´ Turner triples to complete MLB cycle|
|Milestone man Smith headlines Australia´s ANZAC Test squad|
|WATCH: Blue Jays´ Coghlan soars over Molina´s head to score from the air|
|Copa Libertadores Review: Iquique beat Zamora in seven-goal thriller|
|Pochettino hits back at ´enemy´ Xavi over Alli speculation|
|Mourinho: City favourites for top four, not United|
|Sanchez won´t be sold to Premier League rival, insists Arsenal boss Wenger|
|´She is starting at ground zero´ - WTA chief defends Sharapova wildcards|
|Simeone: Atletico have four finals after Villarreal loss|
|Goals are his life - Chelsea boss Conte delighted to see Costa back on target|
|Puel praises former pupil Hazard after Chelsea defeat|
|Carrasco suffers collarbone injury in Villarreal defeat|
|I have a squad of great men - Conte lauds Chelsea toughness in Southampton win|
|A massive step - Cahill, Hazard confident on Chelsea´s title charge|
|Borussia Monchengladbach 1 Eintracht Frankfurt 1 (aet, 6-7 pens): Hradecky and Hrgota heroes|
|F1 ditch ´Halo´ plans for ´shield´ concept|
|Atletico Madrid 0 Villarreal 1: Late Soriano strike downs Simeone´s side|
|Wolves 0 Huddersfield Town 1: Brown seals play-off spot for Terriers|
|Radwanska out of Sharapova´s way in Stuttgart|
|Angers 2 Guingamp 0: Letellier saves hosts from penalty injustice|
|Niasse red card overturned after Hull City appeal|
|Thiem´s dream start in Barcelona|
|Chelsea 4 Southampton 2: Hazard, Cahill and Costa move Conte´s men a step closer|
|Ramos receives one-match ban for Messi foul in El Clasico|
|AFC Champions League Review: Paulinho at the double in Guangzhou Evergrande rout|
|NFL Draft 2017: Texans´ Day 3 picks to be announced from outer space|
|United need Griezmann - Silvestre backs proven goalscorer to emulate Rooney|
|Roma can achieve great things - Serie A club can join Europe´s elite, claims Monchi|
|Mourinho: Manchester derby not about me and Guardiola|
|Rain forces RCB-Sunrisers abandonment|
|Pakistan wrap up dominant first-Test win over West Indies|
|Cavani extends PSG contract until 2020|
|Amsterdam ArenA to be renamed after Johan Cruyff|
|Surgery all that matters for Ibrahimovic - Mourinho realistic on United star´s future|
|Bouchard, Pironkova ruts deepened in Istanbul|
|Ibrahimovic should join me in MLS - Schweinsteiger|
|I cannot guarantee anything - Pochettino puts Alli future aside for Spurs title charge|
|Golf rules changed after TV viewer denies Thompson|
|Schwartzman and Simon fall at first hurdle in Budapest|
|Timely return for Sharapova with Serena out of the equation|
|Azhar earns Champions Trophy recall for Pakistan|
|F1 Raceweek: Hope for struggling McLaren and Red Bull in Russia?|
|Emery expecting full-strength Monaco for semi-final|
|Schweinsteiger has no regrets over Manchester United move|
|Sanchez a slow starter - Wenger|
|Zidane would not change Clasico approach|