Late goals from substitutes Giroud and Aaron Ramsey cancelled out Leicester's 3-2 lead and ensured the Gunners kicked off their 2017/18 campaign on a winning note.
"We kept going and the spirit of the team was absolutely outstanding", Wenger said.
The Serie A side have now said they will not increase their offer and Shakespeare is happy to have Mahrez in the team.
'I prefer to be on the pitch, ' the 30-year-old admitted in his post-match interview with Sky Sports.
Arsène Wenger expressed his relief that Olivier Giroud, widely considered this summer to be either on the move or a player destined to be not much more than a supersub, remains very much at the heart of life at Arsenal. "He is a fantastic guy as well - committed, he loves the club". He doesn't want to leave, but at some stage I opened the door for him because I had many strikers.
"For us it was a bit disappointing with the goals that we've let in and we shouldn't really be conceding in that way, but I think we showed great determination and great togetherness to get back into the game and we won it towards the end of the game".
Wenger also stated that lack of focus on the part of his defenders cost Arsenal the first two goals they conceded.
Vardy had better luck soon after, though, this time climbing highest to pick out the far corner of the net with his head from a corner to double his personal tally for the night.
"We lost the openers in my first and second years at Arsenal so now we were third time lucky".
"We went for a win and we deservedly earned it".