The result lifted Wenger's men back to the top of the Barclays Premier League and provided a good riposte after the other members of the top seven won over the weekend.
Wenger said: "It was a big win for us. We had to give a strong response.
"Everyone looks at you to see if you drop points because they have made their points over the weekend.
"You are a bit more under pressure when you play last because you know you are not allowed to drop points.
"You can only give one answer - to win the game."
Arsenal looked to be cruising towards victory until Benteke, after four months without a goal, suddenly rediscovered his scoring touch 14 minutes from time to set up a frantic finish.
Wenger said: "There were two different halves. The first half was about playing well, the speed of our passing and control of the game. The second half was more about fighting.
"Villa played straight through the middle, a very direct game.
"Maybe we were a little bit too cautious just to keep the 2-0 and it was then about fighting. Our defenders kept us in the game.
"It was a nervous finish but overall you have to say Villa did fight until the end and were committed for every single ball.
"You have to give them credit for that. It is why it was a difficult game for us but I like the fact we are mentally ready for a fight."
England midfielder Wilshere showed his class by finishing off a neat move in style to open the scoring and then providing a perfect pass for Giroud to double the lead.
Wenger said: "He has found his change of pace again.
"I would say his game is about that and his penetration. He is not only a passer but is a guy who is incisive with the ball. It is his strength.
"For that you need to be at the top of your game physically. He is coming back to his best."
The concerns for Wenger were injuries to Tomas Rosicky, who took a blow to the face in a challenge with Gabriel Agbonlahor, and Nacho Monreal, hurt when fairly tackled by Ron Vlaar.
Wenger said: "Rosicky has a bad nose. I don't know if it is broken or not but it looked bad.
"I didn't see it (the incident) and Tomas doesn't know if he did it on purpose or not.
"Monreal I think was an accident. We have to check his metatarsal Tuesday morning. He got a kick on the top of the laces."
- Sports & Recreation
- Olivier Giroud
- Jack Wilshere
- Christian Benteke
- Barclays Premier League