The 22-year-old midfielder was photographed smoking in a hot tub in Las Vegas, the second time in less than a year that he has been pictured with a cigarette in public.
Wilshere spoke to Sky Sports News from Arsenal’s pre-season training in New Jersey, USA and said: “I made a mistake then, and I made a mistake again – people make mistakes.
“I’m young and I’ll learn from it.
“I realise the consequences it has and the effect it has on the kids growing up.
“I’ve got kids myself, and I don’t want them to grow up thinking that their dad smokes and that it’s OK for footballers to smoke, because it’s not.
“It’s unacceptable. I’ll accept the consequences and move on.”
After a disappointing World Cup campaign in Brazil that saw England crash out at group stage, Wilshere is pleased that pre-season is under way and that Arsenal have been taking full advantage of the summer transfer window.
And he says he is ready to get his own career back on track.
“This season is a big one for me," he added.
"I came back to pre-season early to show everyone my commitment and I’m fully committed to the club, and to my job, and I want to show everyone that.
“This year we’ve really been positive, gone into the market and signed a couple of great players.”
One of those players is Chilean Alexis Sanchez, whom Arsene Wenger purchased from Barcelona for an undisclosed fee.
Jack Wilshere watched the 25-year-old impress in Brazil and thinks he, like full-back Mathieu Debuchy, will fit well into the Arsenal set-up.
“You can see what Sanchez did at the World Cup – he was the best player on the pitch.
“They are two great signings and we’re really looking forward to them coming in.”
Arsenal start their 2014/15 campaign on 16th August, at home to Crystal Palace.