Wenger made his claims after seeing his side held to a goalless draw at Villa Park in the Barclays Premier League.
It was a severe dent to the Gunners' title hopes, particularly with Chelsea overcoming Birmingham 3-0 at Stamford Bridge.
O'Neill was clearly upset when told of Wenger's remarks and said: "If that is what he saw, well that is a ridiculous statement. He has made a few ridiculous statements in his time here (in England) and that is as good as any. That is an appalling insult.
"I thought we played splendidly in the game. Their `keeper made a great save from Gabby (Agbonlahor) early on and Ashley Young produced some incredible balls into the box that just needed a touch on them.
"Arsenal caused us problems and we had a bit of luck when they hit the post and crossbar but we did not deserve to lose in this game."