The West Ham boss is a huge admirer of the England international and believes his signature would have helped secure West Ham's Premier League future.
But despite appearing close to a ?2million loan deal for Carroll, who has been deemed surplus to requirements at Liverpool, Allardyce now believes there is no prospect of him joining.
Hair we don't go: Carroll won't be joining West Ham, according to Allardyce
'I would probably have stuck my neck out and said we would almost certainly stay up with him on board,' Allardyce told The People.
'We wouldn't have thought we would have had any chance of signing a player of Andy Carroll's capabilities but it became clear a couple of weeks ago there was a possibility of a loan. Unfortunately at this moment, it's not the case.'
Allardyce also revealed he shed no tears when he saw his former club Blackburn relegated last season.