The 24-year-old made the move to east London permanent for a club record fee that could rise to £17.5million after spending last season with the Hammers on loan from Liverpool.
However, Carroll has yet to line up for Sam Allardyce's side since then, with a foot complaint the latest in a long line of injuries which could rule him out until the new year.
It leaves West Ham light in terms of attacking options, with Modibo Maiga, wantaway Ricardo Vaz Te
and new signing Mladen Petric facing the unenviable task of filling the void.
Maiga has started all four Barclays Premier League matches this season but has failed to score in any, while Sunday's 0-0 draw at Southampton makes it three games without a goal for West Ham.
The side have managed just six shots on target so far this season, but captain Nolan remains confident.
"None of us have criticised (Maiga), that's the main thing," he said.
"I don't think anyone has really criticised him, I think it's just the fact when you miss someone like Andy, you're going to talk about Andy, instead of the centre-forward who's actually playing.
"If he doesn't come in and score goals then it's all 'he's no Andy Carroll'. There's not many people like Andy Carroll, maybe Rickie Lambert, but I think they're a bit different here and there.
"Modibo Maiga's got other strengths, he's very good in the air for such a short lad. He's good on the floor. Very technically gifted, when he's in front of goal he's very calm.
"We've just got to start getting him those opportunities, he's been working so hard I'm delighted with him.
"I think he's been fantastic for us. He's been thrown in at the deep end.
"This boy has come over from Sochaux, he was upset that he wasn't playing a lot, he's knuckled down over the summer and he's getting his chance.
"Now it's up to him to start putting him in the back of the net.
"(Petric) has been training with us but obviously he is a bit behind because he hasn't had a full pre-season.
"He's in great shape coming back, don't get me wrong, but it's just football fitness. He has got to get used to that and hopefully we will have him there or thereabouts for Everton, maybe to come off the bench.
"It is a great acquisition for us - we are very pleased we have got him. He brings a lot of quality and something different. He is another one that we have got to get used to."
Goals have also been a problem for Southampton early in the campaign.
Mauricio Pochettino's side have managed to net just twice so far, with club record signing Dani Osvaldo
yet to gel with talisman Lambert.
"We just needed that goal," captain Adam Lallana said.
"It has been the same story for the first two games. We'll move on because we've got a tough game next week.
"It is a point, we kept a clean sheet so it is a positive. It has not been bad, but it could have been better I think.
"We are creating chances, it's just about turning those telling chances into goals. I am reasonably happy, but it could have been better, you know?
"We have drawn two at home and we would like to win our home games.
"No disrespect to Sunderland and West Ham, but they are winnable games for us so that's what we want to improve on.
"We've got a tough game against Liverpool next week, but we're looking forward to it."