"If we take the game as we played against Southampton or Chelsea, I think we'll win".
The former Liverpool striker's first goal since November put relegation-threatened Stoke within touching distance of their first win in 10 games.
But West Ham roared back and salvaged a potentially invaluable point in the last minute of the 90 when Cresswell's ball into the box was met on the volley by Carroll, who guided the ball beyond a helpless Butland.
Meanwhile, Stoke chief, Paul Lambert, said: "If we'd got the three points, I thought we'd deserved something from the game anyway".
"It is a blow because we were so close to winning. With the atmosphere in stadium, it is a hard place to come but I thought we were excellent". "I couldn't ask for any more from my players", Lambert said. "Regardless of how we do it, we have to get a win but we certainly will drag teams into it".
The Hammers drew 1-1 at Chelsea last week and now return to the London Stadium, knowing that another three points can haul them further clear of the relegation zone.
"We took points off them, though, and it's a point for us, so it's a good result in the end".
It couldn't have come at a worse time with national team boss Gareth Southgate watching from the stands in east London.
Police have warned social media trolls they could be committing a criminal offence by abusing referee Michael Oliver and his wife Lucy.
First, Arnautovic converted Aaron Cresswell's cross, but he had strayed marginally offside.
Playmaker Manuel Lanzini returns to the bench tonight, and joins Adrian, Patrice Evra, Josh Cullen, Jordan Hugill, Andy Carroll and Javier Hernandez as substitutes. On the first occasion Marko Arnautovic was offside when he headed home - and then he was interfering with play from Edimilson Fernandes' shot.
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