Arsene Wenger says his "professionalism or commitment" cannot be questioned but that uncertainty over his future contributed to Arsenal failing to qualify for the Champions League.
It is the first time Arsenal, who finished fifth, have failed to qualify for the competition for 20 years.
Wenger, whose contract expires this summer, says his future will be decided after the FA Cup final on 27 May.
"I have said no to every club in the world," said the Frenchman, 67.
- Chelsea top of the class - Phil McNulty's Premier League end-of-season report
- Kane, Alli, Sanchez, Hazard - Garth Crooks' team of the season
Wenger has been in charge of the Gunners since 1996, winning three Premier Leagues and six FA Cups, but has faced protests from Arsenal supporters this season calling for him to quit.
"I believe since January we have played in a very difficult environment for different reasons," he added.
"Some you know about and that's very difficult for a group of players to cope with that - and some other reasons we will talk about on another day.
"Psychologically the atmosphere was absolutely horrendous. It has been difficult, yes, and certainly my personal situation has contributed to that but you can never question my professionalism or commitment."
Arsenal beat Everton 3-1 on Sunday, but a 3-0 home win for Liverpool against Middlesbrough saw the Gunners finish a point behind Jurgen Klopp's side in fifth.
"I'm a lot more resigned because it's been coming for a few years and everybody has to focus on the FA Cup," former Arsenal striker Ian Wright told BBC Radio 5 live.
"This is done, we are in the Europa League, there is nothing we can do about it."
- Flippers, flappers and triple keepers: The Premier League's weirdest final day?
- REPORT: Arsenal 3-1 Everton
Wenger, whose side face Premier League champions Chelsea in the FA Cup final, said it was "very sad" Arsenal will not be playing in Europe's top club competition next season.
He added: "We do our job and you are professional and part of the job is being professional when the environment is not positive."
Some Arsenal fans also voiced their frustration at majority owner Stan Kroenke.
"I think you respect everyone in life and I respect Stan Kroenke a lot," said Wenger. "It is not his fault we didn't reach the Champions League, it is the technical department's responsibility for that.
"A club works when everybody does their job and we live in a society where everybody has an opinion and what moves society forward is when we work and not talk too much."
Wenger gets support from old rival Ferguson
Former Manchester United manager Sir Alex Ferguson had a sometimes bitter rivalry with Wenger during his Old Trafford reign, winning 13 Premier League titles with the Red Devils.
Scot Ferguson was in charge for 26 years, while Frenchman Wenger is in his 21st year at the north London club.
"At the moment, of course, with the ridiculous situation of the pressure Arsene is under, I just wonder if they realise the job he's done," Ferguson told Sky Sports.
"The most amazing thing about him is this: he has come through a forest of criticism for months now, and has never bowed. He has seen it right through, he has shown a determination, a stubbornness. I think when you look at that, it's a quality, and I'm not sure they'll ever get another manager like that.
"It's quite easy to say 'Get rid of him', but who do you get? Who do you get in to keep that club the way they are for the next 20 years?
"I really feel sorry for him because I think he's shown outstanding qualities, and I think he has handled the whole situation. I don't know many that have done that."
'The toxic mood was on show again' - analysis
BBC Sport chief football writer Phil McNulty at Emirates Stadium
As Arsene Wenger sifted through the fall-out from Arsenal's failure to reach the Champions League for the first time in 20 years, he made a stark admission.
Wenger, reflecting on the atmosphere around Emirates Stadium, said: "The psychological environment was absolutely horrendous."
He insisted he was not using this as an excuse for Arsenal's failings but it was clear he felt the over-arching atmosphere had not helped his players as they tried to fight their way into the Premier League's top four.
Wenger may have a point - but has he himself not made a major contribution to the mood around the club and has to take his share of responsibility as his own Arsenal future became almost a matter for daily debate?
Even now, although most now assume he will extend his stay as Arsenal manager, he was simply saying his own personal situation would be "sorted soon".
The lack of clarity has cast a cloud over Arsenal's season and provided an unwanted sub-plot when matters should have been solely focused on the pitch.
The toxic mood was on show again as Arsenal's fate and the realisation that they would be in the Europa League next season became clearer, with chants against American owner Stan Kroenke, who has ignored a £1.3bn takeover bid from Alisher Usmanov, who has a 30% stake in the club.
Wenger defended Kroenke but it was obvious he feels factors elsewhere have created this "horrendous" psychological environment that has swirled unhelpfully around Arsenal.
The problem for Wenger is that he takes a big portion of the responsibility - and part of the price he and Arsenal will pay is that they will be out of Europe's elite group next season with their noses pushed against the window as they contemplate life without the Champions League.