In the second half, however, Carroll was sent off for catching Chico Flores in the face with a trailing arm and was subsequently banned for three matches.
Ahead of Saturday's trip to Aston Villa, Noble has called on the Hammers side to band together in order to get the required results to climb out of the relegation zone.
"Andy being suspended is obviously a massive miss for us," he told the London Evening Standard.
"For him to be back the way he was and then to miss him for another three games is going to be tough but we have to dig in and get results without him.
"Everyone will have to play their part to try and get us three points away from home.
"We're three points off eleventh, so getting ourselves back in that pack with the win against Swansea was important.
"We're looking up rather than down at the moment and even though we're in the bottom three, I'm sure we can claw our way back."
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