The 57-year-old manager has urged his squad to show they can cope after the on-loan Liverpool striker was ruled out of action until mid-October with a hamstring injury
Carroll is expected to return to the side after the next international break but the Hammers are no closer to knowing when also-injured midfielder Jack Collison will make a comeback.
And Allardyce has challenged his squad to prove they can cope with injuries during the tough run of games which lie ahead.
"It depends on the likes of Carlton Cole and Modibo Maiga stepping in and doing the business, making sure we use the strength of the squad when we need to," Allardyce told Sky Sports.
"We have only got two players injured at the moment, a lot of other teams in the Premier League have more. If that continues, it will help us to be more and more consistent.
"Andy Carroll has only played 68 minutes for us. We have conceded just three goals, all at Swansea, and kept clean sheets in the other games.
"It is not all about Andy, but it is about us trying to perform as a team again on Saturday against Sunderland."
Despite his bullishness, Allardyce did admit that the fitness of Collison is a major worry, with an ongoing knee problem preventing the midfielder from playing.
"Obviously Jack is a big concern because he has not kicked a ball for us yet since the end of last season," Allardyce added.
"He was a major influence in our promotion year so we would love to get Jack back as quickly as we possibly can."