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".
Andy Carroll's last-gasp equaliser spared Joe Hart's blushes after the West Ham goalkeeper made a costly blunder in Monday's dramatic 1-1 draw against Stoke.
The former Liverpool striker's first goal since November put relegation-threatened Stoke within touching distance of their first win in 10 games.
BC-SOC-West Ham-Stoke, 1st Ld-Writethru, 408 Carroll equalizes late as West Ham holds Stoke to 1-1 in EPLAP Photo LON606, LON816Eds: Updates with detail, quotes.
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"If the supporters do what I think they'll do, we just have to turn up and try and get a win".
Lambert reflected afterwards: 'It is a blow because we were so close to winning.
"You need a little bit of luck at certain times but the performances have been incredibly high and the way we have played I couldn't ask for any more from the team".
"If we can do that (beat Burnley), it will set the cat right among the pigeons", said Lambert. "Regardless of how we do it, we have to get a win but we certainly will drag teams into it".
"That decade might be about to come to an end with Stoke six points off safety with only five games to play".
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Oliver and his wife were subjected to social media threats over the incident that led to Juventus's elimination.
And while Hart floundered, Butland did his World Cup hopes no harm with a string of saves, including one with his face from ex-Stoke man Marko Arnautovic's close-range shot.
The Hammers were denied by the linesman's flag moments later when fellow substitute Javier Hernandez struck the ball past Jack Butland, but Carroll was adjudged to have handled inside the area.
On this occasion, he was involved in three disallowed West Ham goals.
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