If a deal cannot be struck with Carroll's parent club, Liverpool, then Allardyce insisted West Ham would have to land a different big-money striker just to maintain the status quo.
"He was very, very good, even with the limited supply we gave him," said Allardyce, who feels that each impressive performance strengthens West Ham's chances of keeping Carroll.
"I think it improves it, personally. Whether it can be done at the end of the season, we have to wait and see.
"It proves we are buying a player that is critical to our development programme.
"We have to be better next season than this season. If we haven't got Andy Carroll next year, we have to produce a big big money signing to get someone of his quality first and foremost, besides the rest that we need."