Carroll, who only made his comeback from a series of foot injuries in November, scored his first goals since March in the 3-1 win over 10-man Swansea City at Upton Park.
The headed double came either side of the interval and helped West Ham move third in the top flight, having fallen behind to an early Wilfried Bony goal.
Manager Allardyce feels Carroll, brought in for a club-record fee last year, can play a role in keeping the club flying high.
"I hope we can carry on being this consistent," he said.
"It was massive for Andy Carroll. He is unstoppable when he gets that space. Hopefully he continues to learn that way. It must be close to his best performance for West Ham.
"He's 100 per cent fit, but there's a little more to come on his match fitness."
Allardyce also lauded Carroll's style of play, with his brace of headed goals underlining his main threat.
"It's got lost in the game somewhat today," he added.
"People don't seem to talk about the technical ability you need to meet a ball that's in the air at the right time and guide it into the right place."
