The Villans shocked the Gunners at the Emirates Stadium with a win on the opening day of the season but, despite Christian Benteke's second-half strike, the north Londoners' quickfire double from Jack Wilshere and Olivier Giroud saw to it that there would be no repeat.
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"It was a big win for us," he told reporters. "The first half was about playing our game with the speed of our passing and controlling the game. The second half was more about fighting - I felt it was down to, first of all, a different style from Villa, who played three through the middle and a very direct game.
"Maybe we were a bit too cautious just to keep the 2-0 but it was about fighting and our defenders kept us in the game. Maybe we thought we'd keep control of the game and keep it at 2-0 but we lost a bit of incisiveness in our game and that desire to score more.
"[It was ] a nervous finish but, overall, you have to say that Villa did fight until the end and were committed for every single ball and you have to give them credit for that."
There was some concern on the injury front for Arsenal when Tomas Rosicky, himself on as a substitute, had to be withdrawn after appearing to be caught by the elbow of Gabriel Agbonlahor, while Nacho Monreal is set for a scan on Tuesday to determine if the left-back broke his metatarsal.
"Rosicky has a bad nose," Wenger confirmed. "I don't know is it broken or not, it looks bad. Honestly I didn't see the elbow, I have to watch it again. [Rosicky] told me that he got the elbow but he himself doesn't know if he did it on purpose.
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Wilshere's goal and assist within the space of a minute proved the catalyst for the win and the Gunners boss was delighted to see the midfielder on his way back to his best.
"He has his change of pace back; his game is about that and his penetration because he's not only a passer but he's a guy who is incisive with the ball," Wenger enthused.
"It's his strengths so, from that, you need to be at the top of your game physically. You see it when you know well the players well in training. In the last games you see that he's coming back to his best."