Allardyce said Monday that the new Financial Fair Play rules in the Premier League next season could "blow the whole deal" for signing Carroll.
Premier League clubs last week voted through new regulations that will limit how much of the new television income can be spent on wage bills and there could even be points penalties for severe breaches of the guidelines.
"So in one fell swoop the financial restrictions mean Andy Carroll can't sign for us from Liverpool because it's too expensive, even if he wanted to," Allardyce said. "Somebody will have a bigger budget than us somewhere, but I tell you that is what's going to happen, I might not be able to afford Andy Carroll, full stop, even if I wanted him, even if the chairmen wanted him, even if we all wanted him, which we do, it will not be allowed to happen."
England forward Carroll, 24, maintains he would have no problems with the transfer being made permanent in the summer, but Allardyce revealed committing to such one marquee signing could just prove too costly.
Allardyce believes it will take some time before the true impact of the new regulations, which have been brought in to try to level the playing field in the top flight, can be felt.
"I suppose across the board when you first introduce something new the fair-unfair scenario has to get sorted out somewhere along the line to find out how you have to tweak it to make it better," he said.
"But if we want Andy Carroll, or any player, and you look at the whole thing, you are going to have to move very quickly now because your budget is going to say that [figure] and you are not allowed to go over that apparently, and because you are not allowed to go over that, you have to say [to the player] 'sorry and off you go', so then it is very difficult to improve your side from last season."
Allardyce, however, expects to extend his own contract past the summer to remain at the Upton Park helm.
"I wouldn't be here if we weren't playing in the Premier League next season," the former Bolton, Newcastle and Blackburn boss said. "I always said if I don't keep them up, I won't stay. We're very close to being mathematically OK. I think it's highly unlikely with four home games in the last six that we're not going to pick more points up.
"We are going to be safe and playing in the Barclays Premier League next season so my planning will be done as quickly as possible and we'll get on to the contract, which I'm sure I'm going to sign," he said.
The 58-year-old Allardyce replaced Avram Grant at the Upton Park helm following the club's relegation from the top flight in the summer of 2011.
Allardyce confounded the critics to take West Ham up at the first attempt via the playoffs and the club now looks all but certain to remain in the top flight after Saturday's 1-1 draw at Southampton.
Information from Press Association was used in this report.