Carroll joined Allardyce's Hammers on a season-long loan basis from Liverpool during the summer transfer window.
The England centre-forward made his return from a hamstring injury during Saturday's 3-1 loss to Arsenal at Upton Park.
Despite seeing his side defeated by the visiting Gunners, Allardyce was left pleased with the problems that Carroll caused the opposition's defence.
"That's why we've got him. He's an unbelievable player and he can only get better," Allardyce told the club's official website. "For his second chance he outjumped the goalie. The goalie can use his hands to catch the ball but he goes and outjumps him.
"Anybody that doesn't fear Andy Carroll is foolish. As long as we can keep giving him the service I think he's going to be a tremendous asset."
Carroll is yet to find the net for his club.