The Gunners boss was left frustrated by defeat to Roberto Di Matteo's Chelsea on Saturday, and felt his new €15 million striker should have equalised in the last minute
After rounding Blues goalkeeper Petr Cech in the last minute of the game, the 26-year-old Frenchman blasted into the side netting with the goal gaping, and the Gunners fell to defeat after failing to capitalise on a cagey display from the visitors.
"[Giroud] was in a good position. Why did he not score? I don’t know," he told reporters. "I felt [he should have scored], yes."
While Giroud's miss was a costly one, Wenger was disappointed with the lack of conviction in his defence, which allowed Chelsea to dominate aerially and eventually score twice from set-pieces.
He added: "I think on the pitch you have to jump for the ball. Especially on the first and second goal I don't think we showed enough authority to attack the ball and that cost us today."
Fernando Torres volleyed in after Laurent Koscielny failed to get close enough to stop him from a free-kick, and the French defender was guilty once again as he deflected a Juan Mata free-kick past Vito Mannone for the second.
Asked whether the dropped Per Mertesacker would have made a difference, Wenger replied: "We don’t know. That's possible. But you don't know. Maybe. Difficult to check. We can't replay the game."
Wenger was left frustrated by the manner in which Arsenal conceded, suggesting his side had done well to contain Roberto Di Matteo's men."
He said: "It was difficult, we played against a good side. Overall it's a shame that we gave the goals away the way we did. In the second half, the first time they crossed the halfway line they scored.
"After that of course it's difficult. They are always dangerous in the big games when you are always 2-1 after the goal you have to open yourself up, you are exposed to counter attacks and that's why we lost the game."
Despite the defeat, Wenger remained optimistic for the future, particularly given the spirit of the squad he has assembled: "I believe overall there's a lot of positives in this game and that's what we have to take going into the next one.
"I'm quite confident because we have a strong spirit and the team wants to do well."