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."
|Torn ankle ligament leaves Halep 50-50 for Roland Garros|
|Ferguson´s 26-year Man Utd reign unmatchable - Wenger|
|Vidal back in Barcelona training|
|South Africa the perfect preparation for England - Root|
|Sanchez future completely Arsenal´s decision - Wenger|
|Lisicki excited for Mallorca return|
|Wenger confident Sanchez will be fit for FA Cup final as Gabriel is ruled out|
|Wenger doesn´t know if FA Cup final is his last game at Arsenal|
|She has served her suspension - Rogers Cup happy to hand Sharapova a wildcard|
|Pique: I have spoken to Carvajal about Real Madrid chant|
|Australia coach Cheika hails retiring Wallaby Mumm|
|Ranieri ´stimulated´ to return amid Crystal Palace and Watford rumours|
|Dele Alli: Tottenham do not need to spend if we keep stars|
|Eriksson: Terry won´t have a problem finding new club after Chelsea exit|
|Monaco? Ferrari can win every race - Andretti|
|Cubs top Giants behind Lester´s complete game, Schwarber´s career-long HR|
|Mayweather v McGregor one of the biggest boxing mis-matches – Leonard|
|Stanley Cup playoffs: Senators force game seven against Penguins|
|Copa Libertadores Review: Lanus advance to last 16 as Chapecoense are docked points|
|Irving lead Cavs comeback against Celtics|
|Celtics star Thomas contemplating surgery for injured hip|
|Australian Cricketers Association to control players´ image rights|
|Montpellier appoint Der Zakaria as coach|
|Madrid boss Zidane will be next France coach, says Leboeuf|
|LeBron James ´focused on the present´ after awful game three|
|Goodell: Brady wasn´t diagnosed with concussion last season|
|NFL moves Super Bowl 55 to Tampa after Los Angeles stadium delays|
|Chapecoense docked three points, knocked out of Copa Libertadores|
|Cellino era over as Radrizzani completes Leeds United takeover|
|Gronkowski, Patriots agree to incentive-laden contract restructure|
|PSG respond to raid reports|
|CAF Champions League Review: Bouazza strikes late for Etoile du Sahel|
|FFF rejects relegated Bastia´s appeal over forfeited Lyon game|
|All Blacks captain Read signs new deal until 2019|
|AFC Champions League Review: Paulinho gives Guangzhou the edge as Kawasaki Frontale impress|
|No worries for Nishikori in Geneva|
|Security stepped up for Brook-Spence in wake of Manchester attack|
|Mourinho leads Man Utd on tour of Friends Arena|
|Allardyce to leave Crystal Palace and retire|
|Carvalhal to stay at Sheffield Wednesday despite play-off despair|
|I hate comparing players - Bosz uncomfortable with Dolberg-Ibrahimovic parallels|
|Suarez Navarro and Stosur set up Strasbourg showdown|
|Kicker in the teeth for Kyrgios upon return from injury|
|Athletic Bilbao announce Valverde departure amid Barcelona speculation|
|Manchester attacks resonate deeply with Ajax´s Schone|
|NFL clarifies legal touchdown celebrations: Snow angels are in, twerking is out|
|Kovac: Eintracht will throw everything at superior Dortmund in Pokal final|
|We have to play the Ajax way to beat Man Utd - Bosz|
|F1 Raceweek: The (energy) drinks are on Lewis, baby joy for Kimi and Nico|
|Europa League final has lost its glow after terror attack - Ajax coach Bosz|
|Barcelona links a compliment for Chelsea´s Azpilicueta|
|Bayern Munich transfer targets already decided, reveals Rummenigge|
|Red Bull Honda to race at Donington after Hayden´s passing|
|Metropolitan Police increase armed officer presence for Wembley, Twickenham finals|
|Bairstow relishing the sterner test posed by South Africa|
|Koke pens bumper Atletico Madrid extension|
|Dumoulin survives untimely call of nature as Nibali wins|
|Real Madrid complete swoop for Flamengo teenager Vinicius Junior|
|Poulter undecided over U.S. Open qualifying, but hopes it won´t be needed|
|Mourinho looking to stay perfect in Europa League final - Ajax v Manchester United in Opta numbers|
|Koscielny banned for FA Cup final after Arsenal´s appeal rejected|
|Bielsa promises attacking football in Lille unveiling|
|Burnley release Barton following betting ban|
|Lopez seals permanent Espanyol switch|
|Gomes can be as good as Iniesta, says ex-Manchester United youth coach|
|England confirm Anderson groin tear|
|Call of nature dents Dumoulin Giro hopes|
|Changes needed at Valencia, accepts new coach Marcelino|
|Crawford purse must be worth the risk for Pacquiao - Arum|
|England, South Africa reassured over ODI security measures|