Wenger's side beat Everton 3-1 but victories for Liverpool and Manchester City on the final day of the Premier League campaign meant they finished fifth with 75 points and will have no Champions League football next season.
Once again some fans inside the Emirates Stadium held up placards calling for Wenger to step down, as well as some criticising American majority shareholder Stan Kroenke.
Wenger, who took over in 1996 and won three Premier League titles for the north London club -- the last in 2004 -- and six FA Cups is out of contract at the end of the season.
He said his future would be decided after next week's FA Cup final against Chelsea and that his loyalty could not be questioned, adding that he had turned down "every club in the world" to stay at Arsenal for 21 years.
The 67-year-old Frenchman said the atmosphere at the club was a contributory factor in his side's failure to finish in the top four -- which means they will play in the Europa League.
"Of course you want to avoid this drama," he said. "I'm experienced enough to deal with it but it was a big handicap for the team because they played in a very hostile environment. More than ever we had to stick together and be strong because it's been very difficult for us."
Wenger appeared to criticise the club's fans who have been split between those loyal to him and those who feel he should leave.
"This group of players are remarkable and deserved to be supported in a different way," he said.
"It is annoying (to miss out) but we had a spell during the season that was difficult and it was difficult for me in my personal situation. We were playing in a hostile environment.
"The players came back stronger in the last two months and I'm very proud of them for doing that."
Goals by Hector Bellerin, Alexis Sanchez and Aaron Ramsey sealed victory for Arsenal on Sunday but they now have a defensive headache for next week's Wembley final against Chelsea.
Laurent Koscielny was sent off for a bad tackle on Enner Valencia while fellow defender Gabriel suffered a knee injury.
"We lost two centre-backs and that's a big blow," Wenger said.
(Reporting by Martyn Herman; Editing by Clare Fallon)
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