Giroud attracted heavy criticism for his profligate showing on Wednesday as Arsenal slumped to a 3-1 loss to Ligue 1 club Monaco, leaving Arsenal with a mountain to climb in the last 16 tie.
But the France striker responded by scoring the opening goal in the 39th minute of Sunday's home league game before Tomas Rosicky's late deflected strike made sure of the points and sent Arsenal back to third in the table.
Arsenal are a point clear of Manchester United in fourth and three ahead of fifth-placed Liverpool in a tight race for Champions League qualification.
"What was very important was that we had a mentally united response and we showed that," said Wenger.
"We are proud of the response that we showed. Our defensive concentration was at a much higher level than on Wednesday night.
"We know that we can do better with the ball but overall what was important for us was to respond with a win. We got it and not everybody can produce that after such a disappointment. It was vital for us, for the rest of the season, to win the game.
"He [Giroud] responded very well and I'm not happy only because he scored a goal, but also because of the workrate he put in from the first to the last minute.
"Olivier's great quality is when his back is to the wall - he has the personality and the character to respond.
"Because I know him better now, that's one of the reasons why I kept him in the team. He acknowledged that he missed his game and he will respond because he has the strength to do it."
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