Carroll is expected to miss a large chunk of the season after he aggravated the plantar fascia tissue in his foot during training earlier this week, landing awkwardly when contesting a high ball.
Allardyce revealed that the England international's injury is more common with the likes of "ballerinas and basketball players" than footballers, and hopes to have Carroll back in action as soon as possible.
"What you find on my research is that this is an unusual injury for footballers. It probably more revolves around people like ballerinas and basketball players because of the bounding side of it," Allardyce told PA.
"What caused Andy's injury in the first place is his leap - he leapt up high for a ball against Reading on the last day of the season and landed [awkwardly on his foot]. That is what happens with basketball players because they are 22 stone and 6'7", it more occurs in those sports.
"Once it has healed, it is about managing it then. Eventually it will be gone, but there is still a period of time after the injury has healed where he will get some discomfort through the foot. We will do all we can to eliminate that as quickly as possible."
West Ham will look to cope without Carroll when they face Southampton on Sunday.