The Frenchman has been questioned recently as his side battle to stay in the Premier League title race and face going without a major trophy this season.
Wenger, in charge since 1996, said he was sick of the constant talk surrounding his future.
"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 said ahead of Tuesday's FA Cup clash against Hull City.
"I have no problem to cope with everything but I find that a bit boring in the end.
"I always have to convince you that I am good enough. I worked for 35 years at the top level."
Arsenal are eight points adrift of leaders Leicester City as their hopes of a first league title since 2004 slip away.
Despite criticism, Wenger said he was disinterested in outside opinions.
"I am humble enough every day to question myself, to accept my mistakes, and believe me I do that," he said.
"After that as well there is no coincidence that the people who own the club tell me to be here for 19 years. Do you think they are more stupid than you or me?
"I am not on Twitter. I don't invite anybody to go out to dinner and be nice with them. I work and work and work and work. If it's not good enough someone will tell me one day.
"That's all I can do. I do not worry what you say about me or what fans say about me. I try to do my job in a proper way and with full commitment. After that everybody has the right to have an opinion."
