The Potters conceded early when Christian Benteke opened for Villa inside five minutes before the visitors responded through Peter Odemwingie, Crouch, Steven N’Zonzi and Geoff Cameron.
After the match, goalscorer Crouch felt that Stoke completely deserved the victory despite letting through the early goal which only had them on the back foot temporarily.
"It was very pleasing the way we played, considering we were a goal down,” Crouch told Sky Sports 1HD.
"At the start of the season we might have collapsed but we showed we've definitely improved.
"We passed the ball really well and we controlled pretty much the majority of the game and came out deserved winners."
Stoke moved up to 10th position with their third win in four outings which extended their unbeaten streak to four games.
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