"Look, I have worked here for 19, 20 years and I'm always sitting here having to justify that I'm good enough to do the job," he told reporters ahead of Tuesday's FA Cup fifth round replay at Hull City.
"What I find just boring is always sitting here after 19 years to face (the question), 'Do you think you are good enough?'. If I am not, somebody will tell me."
Arsenal are bidding to become only the third club in history and the first since Blackburn Rovers in the 1880s to lift the FA Cup three years in a row and Wenger hit back at suggestions that fans were not pleased with efforts on the pitch.
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"I cannot influence the behaviour of the fans," he said.
"How can I do that? I don't know. I am humble enough every day to question myself, to accept my mistakes and, believe me, I do that.
"I try to do my job in a proper way and with full commitment. After that, everybody has the right to have an opinion."
(Reporting by Shravanth Vijayakumar in Bengaluru; Editing by John O'Brien)
