Guy Demel sat out Saturday's 2-1 defeat by Everton due to illness and he was joined on the sidelines by Andy Carroll, Mohamed Diame, Yossi Benayoun and Ricardo Vaz Te.
Long-term injury victims Alou Diarra and Jack Collison were rushed back onto the bench, while Carlton Cole will now be absent for three matches after being controversially sent-off at Upton Park.
The postponement of the Boxing Day match at Arsenal has given West Ham a chance to patch up their players and Allardyce admits the club cannot cope if there are any more absentees.
"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.
"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."