Club-record signing Carroll may have been the sort of individual who could have turned Saturday's 0-0 draw against Sunderland in West Ham's favour, but the England international remains sidelined with the heel injury which has kept him out of the team since August.
West Ham's co-chairman David Sullivan suggested in an interview with Football Focus on Saturday that he would not have sanctioned a big-money move for the 24-year-old if he had been aware of how long his absence would have lasted.
But Allardyce feels his contribution while on loan from Liverpool last season meant it was a sensible deal to conclude.
Sam Allardyce: "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.
"Understanding the size of the investment I can understand why he [Sullivan] 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.
"There is a little bit too much edge in our game.
"Too many simple balls going astray and not getting the sort of pressure on Sunderland we had on Fulham two weeks ago, so we ended up with a dogged affair.
"We wanted someone to find a little bit of genius for us and one of our creative players to pop up with something a little bit special but we couldn't find that today and probably the draw was a fair result."