The 21-year-old was photographed smoking outside a London nightclub in the early hours of Thursday morning as players wound down following Arsenal's 2-0 win over Napoli, with Gunners boss Arsene Wenger later criticising the England international.
Despite the incident Wilshere was recalled to Wenger's starting line-up for Sunday's 1-1 draw at West Brom, scoring the equalising goal which took Arsenal back to the top of the Barclays Premier League table.
Wilshere's 63rd-minute strike was his first league goal in almost three years and he feels he vindicated Wenger's faith in his ability after a week in which he was asked to explain his actions to the Frenchman.
"Players make mistakes," he told Arsenal Player.
"I am not a smoker. I spoke with the boss and he asked me what happened, I explained to him and we sorted it out.
"He put me in the team and hopefully I repaid him. I am not a smoker so I think that will be my last (cigarette)."
Wenger had said ahead of the weekend's meeting at the Hawthorns that he "disagreed completely" with Wilshere's behaviour but was pleased with how the player answered his critics.
"He is an honest guy and when he is wrong he knows it," Wenger said of his midfielder.
"I think today the players don't get away with anything. We got away with it a bit more but they know that's the rules of the modern game.
"They have to deal with it and I think he learns very quickly. What is more interesting for him and for Arsenal is that he shows the right response on the pitch."
England manager Roy Hodgson has said he will not talk to Wilshere about the smoking incident and has also backed the player to star for his country if he is selected for the crucial World Cup qualifying double-header against Poland and Montenegro in the next week.
"I trust Arsene to deal with that situation," he said.
"He will make it clear, I'm sure, to Jack what his responsibilities are. I've had no problems of that nature with Jack, so I don't need to involve myself in it.
"Jack's an Arsenal player who also plays for England. If Arsene thinks it's also good for me to have a word with Jack I'll be more than happy to do so but, as far as I'm concerned, it's Arsenal's responsibility.
"I believe in him, I think he's a very good player, and I'm hoping that he'll turn up on Monday fully fit to play and then it'll be up to me to decide whether I want to put him in the starting line-up."