On-loan striker Carroll is facing a two-month lay-off after suffering a knee ligament injury in the recent defeat at Manchester United.
Cole was brought into the side for last weekend's game against Chelsea and responded with a goal in a 3-1 victory for the Hammers.
Nolan is convinced that he will carry on his fine form and ensure the absence of Carroll is not felt too keenly.
"Carlton has been chomping at the bit to get the chance to prove himself. Hopefully his performance against Chelsea will be the standard he sets himself," the midfielder said.
"I'm sure there will be more of the same coming up, so Andy will not be too missed for us."
West Ham will be looking to push on from a positive start to the season when they take on Liverpool at Upton Park on Sunday.
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