Allardyce made the comments following this afternoon’s 1-0 defeat to Aston Villa away from home in the Premier League.
Tom Cleverley’s goal just past the half-hour mark proved to be the difference between the two sides at Villa Park.
Over the course of the 90 minutes, the visiting Hammers had just 42% of the possession, took five shots of which only one was on target, and earned six corners.
Allardyce was not impressed with West Ham’s display in the final third of the pitch and claimed that they will fail to win again this campaign if they cannot score goals.
"Our cutting edge has been missing for many weeks,” the Englishman told BBC Sport. “We don't have anybody who can score a goal.
“It doesn't matter how many chances we create, we're not scoring. We'll struggle to win a game between now and the end of the season if we can't score a goal.”
The defeat means that West Ham are now 10th in the Premier League table with 47 points from 36 matches.
The London club will take on Merseyside outfit Everton at Boleyn Ground next weekend, before facing Newcastle United away from home at St. James’ Park.