The 22-year-old spent nine months on the sidelines after coming off worse in a 50-50 challenge with Potters defender Ryan Shawcross.
Since then, the former Cardiff City youth player has established himself as a first-team regular for the Gunners, although he struggled to make an impact after first returning to fitness.
However, Wenger believes that Ramsey's critics have urged him on to show his true ability, which has already brought five Premier League goals so far this season.
"[Being out injured] is always an important period in the life of a footballer," Wenger told Sky Sports News. "Can you get back to basics and work harder? Or do you feel sorry for yourself and give up?
"When I saw him respond how he did I always knew he could come back, that's why I kept faith in him.
"He has improved his technique and does not rush his decisions, for example his goal needed a good first touch a and a quick finish, and he did not rush it and showed his confidence."
Ramsey has also scored four goals in the Champions League this season.