With central defensive duo James Collins and Winston Reid already sidelined, Allardyce would have winced when he saw James Tomkins forced off after just 10 minutes with a groin complaint.
With Guy Demel replacing Tomkins, West Ham had no recognised central defender on the pitch and Allardyce felt that cost his side a crucial three points as the Hammers remain inside the relegation zone.
"You try and defend with two full-backs playing centre-half," he said.
"The fact of the matter is it is not their positions and where it is not their positions and you are playing against the Anelkas of the world.
"At the end of the day that is nobody's fault if you are overpowered by the opposition's players. If we had our full quota of defenders fit today we would have won."
Ravel Morrison, Ricardo Vaz Te, Andy Carroll, Stewart Downing and Mladen Petric are also missing for the Hammers and Allardyce reckons he needs to get them fit as soon as possible to turn their luck around.
"It is like drawing a rabbit out of the hat at the minute for me," he said when asked about possible return dates for his crocked players.
"Every day and every week goes by and we have got to get them all fit as quickly as we can, it has been weeks and weeks and weeks for too many of our players.
"That is why we are paying the price at the moment, we used to be great at keeping clean sheets but because of our defensive problems we are finding it hard to do that.
"Finally we have scored three goals at home and we haven't won the game but that is no real fault for the players who played today."
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