But the Gunners could yet secure a place in the Premier League's top four at home to Everton on Sunday, and they can win a trophy when they take on Chelsea in the FA Cup final next weekend.
On their chances on reaching a Premier League top four finish, Wenger whose side are fifth and need Liverpool and Manchester City to drop points said:.
"The most important thing is to win the football game".
After teasing the media over the past few months about what he plans to do, Wenger has finally announced that his future will be decided at a board meeting after the FA Cup final on May 27th. I will be there.
Arsenal last failed to be part of European football's premier competition in the 1996/97 season and go into the final game sitting outside the top four places.
Arsenal will go into this game with Aaron Ramsey and Laurent Koscielny likely available again after injury, but Alex Oxlade-Chamberlain and Santi Cazorla remain out.
"My story, my life", in The Sun, Adams had less than generous words for his former boss Wenger, claiming that coaching from himself could have helped Arsenal a great deal.
Wenger added: "We have to do our job, we are professionals and want to win".
"What Arsenal fans have been through in the last 20 years and in the last 10 in particular is mediocrity", the former striker told BBC Radio Five Live. "What happens to me after that is less important".
The Blues sealed a second title in three years without playing in Europe this term and will finish at least 12 points above Arsenal, who are still battling to qualify for the Champions League themselves.
"And they behave like they want to be at the club".
Watford are dealing with the aftermath of the announcement that manager Walter Mazzarri will leave at the end of the season, and Wenger said: "I'm always sad when managers get sacked". Following ill-fated spells at Wycombe Wanderers, Portsmouth and Gabala, the former England global has now found himself in La Liga with Granada, but will be managing in La Liga 2 next season (should he stay on as manager) after the club's relegation at the end of this season.
"Much as I respected him for his long and successful tenure, my occasional willingness to pass comment on him and the team probably counted against me".