The 23-year-old England striker, who is on loan at Upton Park from Liverpool, has netted just once in 10 outings for the Hammers since moving to London in the summer.
“Andy has only got one goal for us so far and he has to score more,” Allardyce was quoted as saying by the Sun. “All of our forwards have got to get better at finishing.
“The only disappointing thing about our win against Norwich [on New Year’s Day] was the number of chances fluffed.”
The West Ham boss is hoping that Carroll will be available for selection again by the end of the month following a lengthy lay-off with a knee injury.
“I hope it will be no more than three weeks before Andy is playing again,” he continued. “He’s not in full training yet but he’s due to start running this week.”