Matthew Taylor is the latest in a long line of Hammers players to be sidelined after suffering a knock against Burnley in the Capital One victory on Tuesday.
Mladen Petric is also out for a couple of weeks after aggravating an injury in an under-21 team run-out, while Ricardo Vaz Te dislocated a shoulder against Swansea on Sunday.
Together with long-term injuries to players such as Andy Carroll and the fact that the re-signed Carlton Cole is not yet ready for a Premier League start, it has left West Ham's squad depleted as they prepare to face Aston Villa in a vital home encounter on Saturday.
Allardyce, whose side have been drawn against Tottenham in the Capital One Cup quarter-final, said: "It leaves us with a problem in terms of numbers. We're very short of first-team squad players available for Saturday.
"But it's about getting on with the job and using the players available and trying to bring the three points at home that we are looking for."