The striker went straight into Sam Allardyce's starting line-up, following his loan switch from Liverpool, and played an important role, having a hand in all three goals as the Hammers cruised to a comfortable victory.
However, Carroll was forced off with a hamstring problem in the second half, picked up in a challenge with Brede Hangeland, which could see him miss England's forthcoming World Cup qualifiers against Ukraine and Moldova.
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Speaking after the game, West Ham manager Allardyce said it was unlikely Carroll would be able to feature for the Three Lions.
"The real disappointment is Andy Carroll might have tweaked a hamstring which is hugely disappointing if that’s the case. I think it’ll be unlikely he goes now [with the England squad], sadly,” he told Sky Sports.
"He’s desperate to play football. We had Carlton [Cole] ready to go so he was going to be substituted anyway.
“We’ll have to see how it is tomorrow and talk to England and I don’t think he has much chance, sadly for Roy [Hodgson] and sadly for us as well depending on the extent of that damage."
England travel to Moldova on September 7 before heading home to take on Ukraine on September 11.