Gunners manager Arsene Wenger declared on Friday that he "disagreed completely with that behavior" and, despite previous claims that the England international was holding the cigarette as part of a "dare", the 21-year-old accepts responsibility for the error.
"I made a mistake," Wilshere told the club's official website. "Players make mistakes. I'm not a smoker.
"I spoke with the boss and he asked me what happened, I explained to him, we sorted it out and he put me in the team and hopefully I repaid him [by scoring against West Brom]. It's not [going to happen again]. I'm not a smoker so I think that will be my last one."
Wenger had warned his young star that "when you are a footballer you are an example and you do not do things to damage your health... it can damage your reputation as well" but maintained Wilshere would remain a key player as long as he learned from the experience.