Giroud threatened to significantly alter proceedings at the Emirates Stadium when, with his side 1-0 ahead, he was sent off early in the second period for headbutting Nedum Onuoha.
Thankfully for Arsenal, Alexis Sanchez, who had scored the opener after missing an early penalty, turned provider for Tomas Rosicky to grab a second.
Charlie Austin pulled a goal back from the penalty spot, only for Arsenal to hang on and claim the spoils.
Speaking about Giroud's red card, which will earn him a three-match ban, Wenger told BT Sport: "It was deserved. He didn't control himself and that is, of course, a straight red.
"It completely changed the dynamic of the game. We were in control of the game and suddenly we are down to 10 men and only 1-0 up.
"It turned the game from comfortable to a mountain to climb. Olivier is a guy who stands up and admits mistakes. He knows he has made a mistake."
While Wenger was frustrated by Giroud's misdemeanour, the boss could do little but praise strike partner Alexis.
"He always gives you hope that he can deliver a chance," added the Frenchman. "Sometimes he has so much confidence that he is a bit too individual.
"But he is always efficient. He won the penalty, scored the goal and set one up."
