The Hammers have just 14 fit first-team players, with a host of youth team talent joining up with the squad for their FA Cup third-round match at Nottingham Forest on Sunday.
But recruiting new players could prove difficult for Allardyce with his side currently languishing in 19th place in the Barclays Premier League.
Everton defender Johnny Heitinga turned down a move to Upton Park earlier in the week and, although Allardyce remains in the dark on the Holland international's U-turn, he anticipates it will prove a challenge to bring in the right players to help save West Ham.
"I don't know what the real reason is, why Johnny didn't come," he said.
"He just said the morning after it was something he felt wasn't right. That's the only explanation he gave to me. Not something I could extract out of him.
"I knew it was going to be nearly impossible anyway, in this window. As always the window is an impossible scenario to deal with. To have to work in it under the circumstances we have makes it even more difficult.
"Because you have got players who will look around and say, 'Do I want to go to a team in the bottom three? Do I want to go for that fight?' Perhaps some of them will say, 'no. I might as well stay and play the odd game'. You just keep searching and looking."
Monaco striker Lacina Traore is the latest player linked with a loan move to West Ham but Allardyce knows he will be offered players left, right and centre during January.
"I've had more than thousands of calls, it'll probably been millions by the time we finish this window," he said.
"I'd prefer not to have to keep answering my phone every two minutes or every one minute but I do to find out what part of the world these agents have got these players that want to come and are desperate to come to West Ham."
A Capital One Cup semi-final against Manchester City follows the FA Cup tie with Forest but, with just two league points accrued in December, Allardyce admits the mood in the camp is low and that it is his responsibility to lift the squad.
But the 59-year-old also revealed it is up to his grandchildren to keep his spirits up as he plots a path to keep West Ham in the Premier League.
When asked who picks him up, Allardyce replied: "The grandkids at the minute because they're down from the north-east at the moment.
"I spent a few hours with them on the ice rink yesterday at Canary Wharf and I had a nice meal with them after and it lifted my spirits immensely seeing the little ones running around, causing havoc.
"Brilliant, a great afternoon and I really, really enjoyed it."