The Reds had raced into a 2-0 lead thanks to Ryan Shawcross’s own goal and Luis Suarez’s strike, but Crouch and Charlie Adam found the net to make it 2-2 before half-time.
Liverpool captain Steven Gerrard then made it 3-2 from the penalty spot after Marc Wilson was adjudged to have fouled Raheem Sterling, and Suarez fired home his second of the afternoon to again give the visitors a two-goal cushion.
It was a real shame the errors and a penalty that wasn’t cost us
The Potters fought back again through Jon Walters but substitute Daniel Sturridge sealed the victory late on as the Merseysiders moved back into fourth place.
“It was an end-to-end-game, and one we are frustrated not to get anything from again,” Crouch told BBC Sport. “I thought we helped them out with a few sloppy errors.
“To go 2-0 down and then come back showed tremendous character. It was a real shame the errors and a penalty that wasn’t cost us.
“They are great going forward, but we can take a lot of plus points from the game.”
Asked about the penalty incident, ex-Liverpool forward Crouch added: “Marc Wilson said he did not catch Raheem Sterling, and the linesman had a great view and did not give it.”
Meanwhile, Potters boss Mark Hughes was happy with his side’s overall performance despite the defeat.
“I thought we were excellent in terms of our determination,” said Hughes. “There were a lot of big performances, but we had situations that went against us.
“We did not deal with the second goal as well as we should have done, as it was just a big, long ball. I know what group I have here and they showed great character to get back on level terms.
“I felt if we could get our noses in front, it could have been a different game. The penalty decision was key as it swung it back to them.”
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news