West Ham took the lead at Stoke thanks to the striker's opener before capitulating and eventually losing 3-1 to Mark Hughes's side
The England forward opened his account for the season after just five minutes of Saturday's contest at the Britannia Stadium, but the visitors went on to lose 3-1.
Carroll was substituted in the final seven minutes as he still lacks match fitness after suffering with a number of different injuries this term.
But Allardyce believes the former Liverpool man can play an integral role for his side once he gets back up to full speed.
"If we can keep him fit, we can play off him, he can hold the ball up and score goals," the West Ham manager said.
"His match fitness is not quite there, only games can bring it.
"We have got another game next week (versus Manchester United), then quickly get the Hull City game in - Andy playing and resting will be the best thing for him, the more matches he plays they sharper he will get."
The defeat leaves West Ham 12th in the Premier League and still very much in the relegation shake-up, with a six-point gap to 18th-placed Sunderland, who have played two fewer games.