Fans at the Hull game unfurled a banner that said, "Arsene, thanks for the memories but it's time to say goodbye," provoking a defiant response from the Frenchman.
"I don't care," Wenger told reporters after the game.
"Look at the history of the club... and you will see that I have nothing to be scared of. I do not want to speak about that because it is always the same story. It is enough now."
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Arsenal are third in the table, eight points behind leaders Leicester City and three behind derby rivals Tottenham Hotspur, after a run of three Premier League games without a win.
They also face elimination from the Champions League at the last-16 stage for the sixth year in a row unless they can overturn a 2-0 first-leg deficit when they travel to Barcelona next week, but Wenger insisted the team would keep fighting.
"We judge the season afterwards and I'm quite amazed so many people judge it so early," he added.
"We have not given up anywhere and you will see that in the coming weeks. This club has been in a much worse position than it is today."
(Reporting by Simon Jennings in Bengaluru; Editing by John O'Brien)
