The former England international came off the bench to fire the Potters in front in the 79th minute, but a last-minute strike from Andy Carroll pegged the visitors back.
After the game, Crouch expressed his disappointment with the result, but took heart from the improvements his side is showing of late.
"We showed a lot of fight and a lot of character, and we are no longer shipping goals like we were," Crouch told Sky Sports News. "I think we were unlucky tonight."
The draw leaves Stoke second from bottom in the Premier League, five points from a position of safety, while the Hammers are seven points better off in 14th.