Olivier Giroud had given Arsenal an early lead before Christian Benteke headed Villa level after his initial spot-kick had been saved by Wojciech Szczesny, who had brought down Gabriel Agbonlahor.
Laurent Koscielny was then penalised in the second half for felling Agbonlahor, with Benteke scoring the resultant penalty, before the Arsenal defender was later sent off.
Antonio Luna's late goal compounded the misery for the Gunners and left manager Wenger questioning the performance of referee Anthony Taylor.
"It was a huge surprise to me," Wenger told Sky Sports regarding the second penalty. "But more than that, there were many other things that were really disturbing in the game today."
When asked if it was in terms of the decisions and the way the game was refereed, Wenger replied: "Yes."
And asked to elaborate, Wenger responded: "No, because I'm not interested and it's not my job. Despite that, there was room to win the game and that's what we have to focus on."
The Arsenal fans expressed their dissent at the final whistle and there were banners displayed during the game calling on Wenger to spend in the transfer market.
Free transfer Yaya Sanogo is the only arrival at Emirates Stadium this summer, but Wenger will only spend the money wisely after seeing two bids rejected for Liverpool striker Luis Suarez.
He continued: "We are there to buy players if we find the right players, but we are not the only ones working on that.
"It's not my money, it's the money of the club, but we are ready to spend it when we find the right players.
"We are a team who are focused and I believe as well we could have won the game with the players that are on the pitch, and that's the most important thing to focus on."