The Gunners travelled to Aston Villa on Monday night, with Jack Wilshere and Olivier Giroud scoring within the space of a minute to put the visitors comfortably ahead before Christian Benteke headed home to ensure a tense finish.
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"We had to give a strong response because everybody looks at you to see if you drop points because they have made their points over the weekend.
"We were a bit more under pressure when you play last. You know that you're not allowed to drop any points but you can only give one answer and that is to win the game."
Asked his reasons for not including Ryo Miyaichi in the squad for the fixture at Villa Park, Wenger insisted that he made the decision to include Alex Oxlade-Chamberlain instead of the Japanese winger.
He added: "He's [Miyaichi] not injured, he was not in the squad. You know Oxlade-Chamberlain is back and I decided to put him back in the squad and that's why he was not involved."