"We kept going and the spirit of the team was absolutely outstanding", Wenger said.
The goal also continued Lacazette's phenomenal record in the first game of top-flight seasons over recent years - one he might need to add to after Leicester forwards Shinji Okazaki and Jamie Vardy turned the game on its head.
Leicester's heroes of 2015/16 teamed up to give Leicester a 3-2 lead after the restart when want-away Leicester playmaker Riyad Mahrez set up Vardy for his second of the match.
Olivier Giroud headed home the late victor on Friday.
They have won trophies in each of their last two competitive games, beating Chelsea in the FA Cup final last season then in the season opening Community Shield at Wembley.
After enduring a troubled campaign marred by fan protests against him last season, Wenger desperately needs a strong start this term.
"We wanted to do that today - unfortunately that didn't happen and it's something where we can look back and analyse the game and see where we went wrong and improve on the situation".
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. They all deserve to play. "He is a fantastic guy as well - committed, he loves the club. He doesn't want to leave and I'm happy he wants to stay".
Cech admitted it was a sloppy display from the Gunners' rearguard, but he took heart with the way they recovered to snatch the points. "He has a big weight in the squad and it was a relief for me that he made a decision to stay". "There were hard moments when we were down and we managed to get out of that and it's great to see".