Hammers co-chairman David Sullivan was critical yesterday of their £15 million outlay on the centre-forward.
But Allardyce said: "Understanding the size of the investment I can understand why he said that.
"But he also said that only at the end of the season we will be able to judge whether Andy Carroll is a good player or not.
"Andy has to get fit and prove what he can do what he did last season for us. He's the difference between us winning more games and not.
"If you look at our win ratio with and without him it was pretty obvious we had to sign him. It's like Man City not having (Alvaro) Negredo or (Sergio) Aguero.
"We have not overcome the situation without him being fit like we'd hoped we would.
"But once Andy is fit he'll make us better, there's no doubt about that."
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