Supporters launched their attack on the Gunners boss after he replaced Olivier Giroud with Francis Coquelin with two minutes remaining. Wenger refused to comment on that outburst or why he made the change but he was in a fighting mood when asked about the chants in his post-match press conference.
He said: "I don't want to comment on that. I do my job and do my best for the club. I leave it to you to judge. I try to be as good as I can be."
He added: "Is it hurtful? Look, I have managed for 30 years at the top level and I have to convince you I can manage the team? How many games have you managed? I promise you if you manage one I will sit in the stands and chant 'you know what you are doing!'"
When questioned about the substitution, Wenger said: "You can discuss every substitution. You think what you want. I do my job and I let people judge it. I do that every day and I do my best every day. I know why I do it.
"What is the thinking behind the substitution? I will not explain every decision I make, you judge the game for the papers and I sit here and explain to you our game."
Wenger defended his decision not to play Jack Wilshere after the midfielder's long injury lay-off, given the wet and windy conditions, and he said: "I decided that Jack was to be rested today and to not bring him on. It's more dangerous to bring him on in weather like that when he's tired. It made sense for him not to play today."
Villa boss Paul Lambert, who watched the game from the stands because of a one-match ban, was full of praise for his side's performance - which moved them out of the bottom three.
He said: "We've played the two Manchester clubs and Arsenal in back-to-back games and it's a tough thing mentally. But I thought we played really well today. We were excellent and might have nicked it.
"We defended really strongly. We are playing really well. We are a young side which is growing together and the way we are playing, we are a threat."