The 28-year-old has managed to win an England call-up. Bothroyd was sold by Arsenal ten years ago, for disciplinary reasons.
Wenger said: “He is one of my regrets, he left very early.
“But I have said many times it is important a guy has a good career, even if he goes somewhere else.
“It is better than to play in the reserves.
“He went down but has come back up again and we are all very proud of him at Arsenal.”
He added: “Sometimes it is only later they realise they not only have to have talent, but need to work as well.
“Sometimes to go down to the Championship, there is no better education.
“It is true, he had a little outcome that you can have when you are 16 or 17 but he is a good guy, and he is classy; left-footed, strong body, fantastic technique.
“The incident didn’t happen in the first-team group, it happened in the youth team.
“Liam Brady is responsible for that. They made the decision and I didn’t stand in the way because it was a disciplinary matter.”