"With the atmosphere in stadium, it is a hard place to come but I thought we were excellent".
After a crucial home win over Southampton and a well-earned point at Chelsea, David Moyes' West Ham side were in confident mood and could have broken the deadlock after 55 minutes when former Stoke forward Marko Arnautovic directed a powerful header past Butland but was adjudged to be in an offside position.
Paul Lambert admits that West Ham's late equaliser in the 1-1 draw at the London Stadium was a "blow" for Stoke City's survival hopes.
Carroll, who came in as a late substitution, brilliantly volleyed home a ball from Aaron Cresswell in the 90th minute. The intent is to go and win and we will do everything we can to get three points.
"Wear them down, get the goals late on but the game changed when they got the goal". And we played around with it, it wasn't rocket science. "A win on Sunday would really set the cat among the pigeons".
Things are pretty rosy for West Ham at the moment after their point at Chelsea gave them a bit of breathing space above the bottom three.
"I didn't feel sharp", said Carroll of his return from injury.
"It fell right into my path on my left foot, I swung a leg at it and it went in".
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Only Stoke (63) and Watford (60) have conceded more league goals this than West Ham (58) this season.
It couldn't have come at a worse time with national team boss Gareth Southgate watching from the stands in east London.
Chances were far and few in the opening stanza, however, Stoke keeper Jack Butland made a massive stop in the first half on Marko Arnautovic when the ball struck the face of the England worldwide.
Police have warned social media trolls they could be committing a criminal offence by abusing referee Michael Oliver and his wife Lucy.
On this occasion, he was involved in three disallowed West Ham goals.
Referee Michael Oliver was in charge of his first match since he caused a storm by giving Real Madrid a controversial penalty and sending off Juventus goalkeeper Gianluigi Buffon in the Champions League last week.