Braces from Olivier Giroud and Theo Walcott saw Wenger's men to a 4-0 victory in the fifth-round replay on Tuesday, but a banner reading 'Arsene, thanks for the memories but it's time to say goodbye' was held aloft by visiting fans.
Wenger has grown bored over speculation surrounding his future and the latest situation was of no greater concern.
"There's nothing disappointing for me - I do my job," the Frenchman said.
"Look at the history of the club, since the club exists, and you will see that I have nothing to be scared of."
While Arsenal are into a quarter-final clash against Watford in the FA Cup, they appear set to be unsuccessful again in the Premier League and Champions League.
As to why the fans illustrated their displeasure, Wenger said he was unfazed.
"I don't care. I do not want to speak about that because it is always the same story," he added.
"I told you already sometimes the press conferences are very boring and it is enough now.
"If you have any questions, you ask anybody else but you don't come back to me with that."
