The French boss was heavily criticised for his team selection for Saturday's round-five match against Championship side Blackburn Rovers at the Emirates Stadium - a match that the Gunners lost 1-0.
However, when asked by reporters for his reaction about the digs that followed the Blackburn defeat, Wenger was angry.
"I've been accused of not taking FA Cup seriously. I've won the FA Cup four times. Who has won it more? Give me one name," he said.
Wenger's successes in the competition came in 1998, 2002, 2003 and 2005.