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."
|Griezmann vital to Atletico Madrid´s global ambitions – Garcia|
|Judge continues to star, Stroman leads Jays|
|Kalac: Totti would find it difficult in A-League|
|Mexico 1 Ghana 0: Hernandez sinks African visitors|
|De Boer: I binge-watched Netflix after Inter sacking|
|Ronaldo confirms birth of two sons|
|Saul won´t be leaving Atletico as Cerezo confirms talks with Ibrahimovic´s family|
|Warburton to captain Lions as Sexton, Farrell named to start|
|Paul puts Rockets in ´weapons race´ with Warriors and NBA elite - Morey|
|Lions pair North, Henshaw to miss rest of tour|
|The symbol of Sweden – Ibrahimovic offers sneak peek of statue|
|Thomas takes shot at Miller ahead of Quicken Loans National|
|Portugal penalty flops are still heroes - Santos|
|Chapecoense to play Barcelona in Joan Gamper Trophy on August 7|
|Chile triumph down to Bravo penalty preparations - Pizzi|
|Chile penalty hero Bravo: I was injured!|
|Barba debut on hold after St Helens appeal fails|
|Slumping Yankees send Holliday to DL|
|Bravo the shootout hero as Sanchez, Ronaldo scrap fails to inspire|
|Froome hoping to agree extension by Grand Depart|
|Portugal 0 Chile 0 (aet, 0-3 pens): Bravo the hero in shoot-out victory|
|Paul confirms Rockets trade with heartfelt farewell to Clippers|
|Bolt disappointed despite Ostrava victory|
|Strycova routs Muguruza, Kerber grinds out victory|
|Djokovic into Eastbourne quarters as rain causes further backlog|
|Confederations Cup Diary: Mexico´s preparation glitches, howling in Kazan|
|FIA to further investigate Vettel-Hamilton clash|
|Manchester United striker Rashford snapped with ´king´ Ronaldinho|
|Boro flop Fischer completes Mainz move|
|Naholo and Lienert-Brown in for All Blacks as injuries force Hansen´s hand|
|Clippers send Chris Paul to Rockets to team up with James Harden - report|
|Karsdorp seals €19m Roma switch|
|DFB calls for WADA to take independent control of football drugs testing|
|Britton signs new Swansea deal|
|Liverpool target Keita wants move to Barcelona, Madrid or City|
|Joshua-Klitschko II could be heading for Las Vegas|
|Man Utd and Liverpool target Sessegnon signs first professional Fulham deal|
|Gomis set for Galatasaray switch|
|Warriors´ Stephen Curry to play at Ellie Mae Classic|
|Cowboys rookie Taco Charlton lands inevitable taco endorsement|
|Difficult to motivate goalkeepers in Neuer´s shadow - Kahn|
|Confederations Cup Social Diary: Kuranyi prepares Chile for Ronaldo and Bravo remembers how to be a|
|Former Chelsea and England midfielder Parker retires|
|Carles Alena agrees new Barcelona contract|
|Germany cannot rest on laurels - Low cautious over gifted generation|
|Martial rejects reports he will leave Man United|
|Germany young but experienced - Osorio gets to heart of the matter|
|We must teach fans about discrimination before World Cup, says Smertin|
|Real Madrid ´meet regularly´ with Chelsea goalkeeper Courtois´ agent|
|No solid ground to question Russia, Qatar World Cups – Samoura|
|Knicks part company with Phil Jackson|
|Scorpion kick goalkeeper Higuita joins Atletico Nacional|
|FIFA´s Samoura wants to eradicate doping in football|
|Djokovic loving Eastbourne debut as Wimbledon looms|
|Modeste move to Tianjin Quanjian off amid Aubameyang speculation|
|Bristol City seal club-record signing Famara Diedhiou|
|Germany boss Low wants names in Russia World Cup doping row|
|Hillsborough: The CPS charges|
|Van Dijk and Cedric ´not for sale´, insist Southampton|
|Former Origin and Australia half-back Gidley to retire|
|Saul Niguez has no intention of swapping Atleti for Barcelona|
|David Duckenfield one of six to face Hillsborough charges|
|You can practice penalties too much - Low wary over Germany shootout reputation|
|Fabio Borini set for medical as AC Milan move nears|
|Brazil great Ronaldo ´almost certain´ Cristiano will stay at Real Madrid|
|Davis Cup and Fed Cup combined as ITF announces World Cup of Tennis|
|Bony determined to prove his worth at Manchester City|
|Murray leads Wimbledon seeds for title defence|
|Neville shocked by Wayne Rooney decision delay|
|Ceballos denies Real Madrid deal complete|