Welbeck, who also missed the Euro 2016 due to the injury, made his first appearance of the season as a late substitute in Arsenal's 2-1 victory over Preston North End in FA Cup third round on Saturday.
"I think he went through certainly desperation because the setback he had was absolutely atrocious," Wenger told the British media.
"The patience you need when you're that age - and to miss the European Championship on top of that, after missing the start of the season - it was terrible.
"But he worked hard and certainly it will make him stronger, what happened to him."
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Wenger also said the 26-year-old was allowed to spend some time away from the club during his rehabilitation.
"We let him go outside as well and mixed his time," he added. "At the end of the day, when something like that happens to you, you have to deal with it on your own, but of course we spoke with him a lot and tried to support him."
(Reporting by Hardik Vyas in Bengaluru; editing by Sudipto Ganguly)
