Substitute Giroud handed Arsenal a 4-3 win over Leicester City on Friday night after the Gunners twice fought back from going behind to earn three points.
Arsenal splashed out £52million to bring Alexandre Lacazette to the Emirates this summer, with the new signing breaking the deadlock within the first two minutes.
— FOX Sports Asia (@FOXSportsAsia) August 11, 2017
But fellow Frenchman Giroud decided to fight for his place with the Gunners, rather than head elsewhere, and he made his presence felt with an 85th minute winner.
"I opened the door for him at some stage [to leave] because I know that it's important for him to play," said Wenger.
"But I don't want him to go. And in the end he decided to stay and it was one of the great days of the recent weeks for me.
“Because I know how important he is, not only as a player – he is a fantastic player – but as well in the group.
— Arsenal FC (@Arsenal) August 11, 2017
"He has a big weight in this squad, and it was a relief for me that he decided to stay."
While Arsenal’s strength in depth up front secured a memorable win on the first day of the Premier League season, their defending left much to be desired, albeit they were without centre-halves Laurent Koscielny, Per Mertesacker and Shkodran Mustafi.
"I feel that the goals we conceded, we can work to get rid of that," added Wenger.
"Because one was a corner, one was a goal where we lost the ball in the build-up and the third goal was a corner again.
"So we conceded two goals from corner, we were quite good last season on corners. I feel that with a bit of work we can get that out of our system."