Hammers boss Allardyce insisted he could not risk losing any more players during the festive period as he faced up to the prospect of Carlton Cole being banned for three matches after Saturday's controversial 2-1 Premier League defeat to Everton.
Referee Anthony Taylor infuriated Allardyce and West Ham's fans by sending off Cole for catching Leighton Baines with a raised boot while making what appeared an innocent attempt to control a dropping ball.
Taylor completed his conversion to pantomime villain by dismissing Everton's Darron Gibson for a similar offence in stoppage-time, Hammers supporters pouring scorn on what looked to them an obvious attempt to even up the score.
Allardyce and opposite number David Moyes confirmed they would appeal their players' red cards but the former was equally concerned about how to manage the rest of his depleted squad.
Andy Carroll, Mohamed Diame, Yossi Benayoun and Ricardo Vaz Te were joined on the sidelines by the ill Guy Demel on Saturday, with Allardyce forced to select an 80% fit Gary O'Neil in his starting line-up and long-term injury victims Alou Diarra and Jack Collison on the bench.
"We had 10 players who were fit and one was about 80% fit and that was all we had," Allardyce said.
"We had Jack Collison, who hasn't kicked a ball since the play-off final and Alou Diarra, who hasn't kicked a ball in three months, that is how bare bones we are at the moment."
West Ham's Boxing Day match at Arsenal has been postponed because of a planned tube strike, with their next game at Reading on Saturday, and Allardyce added: "Medical staff are busier than us as coaches at the moment. We can't afford any more contact or any more injuries, so we can't even do any training.
"If we try to do any training and try to do any shape or build-up for Reading, we will get contact between players and, if you get contact between players, you risk injury and we can't do that.
"We can't even get out on the field and do a bit of coaching at the moment."