Giroud had been replaced after missing a number of chances during the 3-1 Champions League defeat.
But Arsenal manager Wenger kept faith in the forward as his side bounced back in the Premier League with Giroud scoring the first in a 2-0 victory over Everton at the Emirates Stadium.
The manager said: “Oliver has one great quality when he has his back to the wall. he has the personality and the strength to respond.
“Because I know him better now, it is one of the reasons I kept him in the team. Because he was not one out, he acknowledged that he missed his game and when he is conscious of it, he will respond because he has the strength to do it.
“I think he responded very well. I am not just happy because he scored a goal but as well for the work-rate he put in today from the first to the last minute as well.
“He is an important player in the box with his presence up front. Even defensively. He played only an hour the other night so those ingredients were important in my decision to select him.”
Giroud put Arsenal ahead in the 31st minute and Tomas Rosicky wrapped up the victory that keeps Arsenal third with a deflected 89th minute effort.
Wenger added: “I am very proud of the response we have shown today. Our defensive concentration was at a much higher level than on Wednesday night. We know with the ball we can do better but overall what was important for us was to respond with a win and we got that.
“Not everyone can produce that after such a disappointment and it was vital for us for the rest of the season to win the game today.”
– praise for Paulista –
Wenger handed a first Premier League start to Gabriel Paulista and the defender drew praise from his manager.
Wenger said: “He had an encouraging performance overall. He was once or twice surprised by the intensity of the challenges but overall he made as well, especially in the first half, a great tackle against Romelu Lukaku in the box. He was highly focussed. A good concentration level. He is quick.”
Everton manager Roberto Martinez was left frustrated after a defeat that means his side have won just once in their last eleven league games.
Nonetheless, Martinez sees grounds for optimism and insists his side is improving.
He said: “I think the second goal was a reflection of our season. We have six players in good positions and it ends up in the back of the net.
“You read the 2-0 scoreline but it doesn’t reflect our game and that’s story of our season. We have never had the momentum you need to win games by doing enough. We have had to be perfect to win games and that is something we have to change in the next eleven games.
“Maybe a bit harsh but when we came back in pre season we had incredible high hopes of being able to carry on where we finished last season.
“But we had two games when we dropped four points in the last minutes and psychologically it felt very, very tough to enjoy our football. It’s been more of a chore having to get those points and I don’t see that enjoyment in the league.
“But I do feel the group is becoming stronger. The dressing room now is really down, something we shouldn’t be sharing after a performance like that at Arsenal, but young players going through these experiences could be the final tick for fulfilling our potential and becoming a winning team.”