Andy Carroll, James Collins and Winston Reid were all forced to leave the field with injuries during last weekend's 2-0 defeat at Liverpool.
Allardyce did his best to bring in defensive cover prior to the transfer window closing on Monday, while West Ham also attempted to loan Emmanuel Adebayor from Tottenham, only to fail on both counts.
Speaking at a press conference on Friday, Allardyce highlighted the problems he is facing ahead of a busy period that will see the London club take on Manchester United, Southampton and West Brom in the space of seven days.
"Our injury problems are worrying. Reid, Collins, [Guy] Demel, [Doneil] Henry, [Diego] Poyet and Carroll lie in our medical room at the moment," he said.
"We're not sure how many of them will make Sunday and it's a big, three-game week for us.
"We went all out to secure a central defender after Liverpool, but however hard we tried we couldn't pull it off."
Allardyce had earlier elaborated on his deadline-day frustration in a column for The Evening Standard.
In addition to discussing his failure to sign a defender, Allardyce expressed sympathy for Carlton Cole, who saw a proposed move to West Brom fall through minutes before the transfer window closed due to the collapse of West Ham's move for Adebayor.
"It has been reported that Carlton had a rant at me on the phone and that was right. There's nothing wrong with that - he was entitled to give us a b*****king," wrote Allardyce.
"He'd just been offered a long-term deal at West Brom while his contract with us is up this summer and he doesn't know whether he will be given another one.
"Add to that he would probably have played a lot more football at West Brom than he would have done here.
"Matt Jarvis, at one stage, could have gone to QPR but didn't and that’s one reason why I have absolutely no time for this transfer window, it disturbs so many people midway through a season.
"In the end though, both players are good professionals. Carlton came to see me on Wednesday and said: 'I'm going to have to get on with it.' That's the right attitude and the same for Matt. He will get another chance this season and he has to try and take it better than the others he has had so far this season.
"Quite frankly, deadline day for me was terrible. I was on the telephone all day - in fact most of the weekend after the Liverpool game - the problem was that either the deals were too expensive or the players we were interested in wanted permanent deals rather than loans, which the club favoured."
