We've got five minutes left, it would have been vital 3 points, a lifeline.
Carroll, out injured since the turn of the year, was sent on as a last throw of the dice by manager David Moyes with West Ham trailing to Peter Crouch's goal.
Ten minutes into the second half, Stoke carved out their first chance of the game when Moritz Bauer raced to the byline before picking out Mame Biram Diouf, who fired over the crossbar from close range.
With the tempo rising, Arnautovic hit the target with a powerful near-post drive only to find Butland in the way, the England goalkeeper in flawless position to block the effort with his face. "If it's a shove in the back, it's a penalty, but we played on and he (referee Michael Oliver) didn't give it and, in the end, it's a point, so we'll take it".
West Ham had seen two goals ruled out for offside - both Marko Arnautovic and Edmilson Fernandes were denied the honour of opening the scoring - in the second half before Crouch struck.
David Moyes's side had two goals correctly ruled out for offside and Aaron Cresswell forced two fine saves out of Jack Butland with free-kicks, before the Potters scored what appeared to be the victor through Peter Crouch 11 minutes from time.
But West Ham showed all their fighting qualities as they rescued a point in added time when Carroll volleyed a cross from Aaron Cresswell past Jack Butland into the corner of the net.
The Hammers thought they had won the game when Javier Hernandez scored in injury time, but it was disallowed for a Carroll handball in the build-up.
- On home soil, West Ham have lost just one of their last seven top-flight games (W3 D3), after losing three of the six before that (W1 D2).
- This clash produced 36 fouls, a joint-high tally in the Premier League game this season (level with Chelsea v Manchester United on November 5). "We'e playing well, we have an incredible support behind us, and I'm pretty sure come Sunday, there won't be many stadiums rocking the way ours can rock".
Lambert's only Premier League victory came in his first match against Huddersfield on January 20, but he is insistent that they have been unlucky in recent fixtures.
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