Allardyce worked with Carroll during his time at the London Stadium, and was impressed by the target-man striker.
But Allardyce says that it is very sad that Carroll’s injury has been disrupted so badly by injuries.
“Everyone would use Andy Carroll more if he could stay fit,” Allardyce said.
“That’s the sad thing about Carroll’s career and his time at West Ham. He’s so brave and fearless that sometimes he goes into areas that nobody else would go to.”
Carroll was used frequently by Slaven Bilic, but he has not been in blistering form this season.
Carroll has not scored a goal for West Ham so far this term, despite featuring seven times.
Carroll is currently fit and raring to go though, and could be used in Moyes’ first game in charge, which comes next weekend.
West Ham are set to take on Watford after the international break comes to an end, and the pressure will be on Moyes to get off to a fast start with his new side at Vicarage Road.