The draw leaves Stoke on 28 points from 34 games, level with Southampton and five behind 17th placed Swansea City who both have a game in hand, while West Ham are 14th with 35 points.
Crouch's 79th-minute goal had looked like giving the Potters a smash-and-grab victory when Hammers goalkeeper Joe Hart, in front of watching England manager Gareth Southgate, spilled Xherdan Shaqiri's fierce shot.
But fellow substitute Carroll, in his first appearance since January, volleyed home a last-minute equaliser.
Javier Hernandez soon rifled home what might have been a Hammers victor, but Carroll had handballed and no goal was given.
It was the third goal they had ruled out in the game.
However, the West Ham boss believed his side should have wrapped the game up long before the late drama. We had good moments, good chances and we've been playing well.
Shortly after Moritz Bauer produced a brilliant run and cross for Stoke striker Mame Biram Diouf, who could only scuff the ball over the cross bar.
But this will feel like another loss, having come so close to only a second win in his reign.
Lambert had to be courageous and he was when he brought on 37-year-old Crouch for midfielder Moritz Bauer, who is usually a defender.
The draw lifted West Ham seven points clear of the relegation zone, leaving the Scotsman reasonably satisfied with his sides toil over the past three matches: "I think the points we have taken in recent weeks have been really important".
Stoke is likely to need at least three wins from its final four games to stay up.
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IPL 2018: Gambhir returns to Kolkata as skipper of Delhi
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