However, Allardyce believes that, based on Carroll's performances during his loan spell at Upton Park last season, the £15m purchase from Liverpool was a no-brainer.
"David Sullivan said that only at the end of the season will we be able to judge if Andy Carroll is a good player or not," Allardyce told reporters. "Understanding the size of the investment I can understand why he said that.
"We have got to get Andy fit and Andy has got to do what he did for us last season. It is not his fault he is injured - we have just got to get him fit and keep him fit.
"He is the difference between us winning more games and not, he certainly was last year. If you look at our win ratio with Andy Carroll to our win ratio without him it was pretty significant and pretty obvious that we had to sign him."
Carroll, who scored seven goals in 24 Premier League appearances for the Hammers last season, is currently out of action with a broken foot.
He is expected to return to action within the next three weeks.