The Gunners playing without Nigerian forward Alex Iwobi, who was an unused substitute, got off the mark through their record summer signing Alexandre Lacazette who headed in Mohammed Elneny's teasing cross in the fifth minute into the bottom-left corner.
Vardy scored again on the other side of halftime after 56 minutes to put Leicester ahead once more.
"Giroud is fantastic. I opened the door for him. We had some avoidable goals which we conceded and overall we have to work on that", he said.
"It was good. Obviously I'm still getting used to the English game, the positives and negatives, shall we say, but I'm learning".
Giroud, who had a hard time getting into the starting XI last season as Wenger preferred to play Alexis Sanchez as the lone striker, has been vocal in his desire to play more games from start.
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"There is no chance he could before the window closes. He's really loved here and in the end he chose to stay".
However, Arsenal's lead didn't last long as Shinji Okazaki hit back with a header only three minutes later after Harry Maguire nodded the ball back into the box.
Carragher was speaking shortly after Giroud had helped Arsenal to an incredible comeback win against Leicester at the Emirates. He'll play 30 games, he'll give you 15 goals.
"I'm always looking for the positives, we came to the Emirates and the players executed the game plan". You can not keep the strikers happy when they don't play.
"You would like him to give that but once he gives it we have to defend the second phase better".
Wenger, for one, was very impressed after Friday's victory over Leicester where we came from behind to snatch victory from the jaws of defeat.
"I think we have all seen the amusing business of the transfer window and we never know what is round the corner".