James Collins' hamstring injury suffered in the 3-0 defeat at Sunderland means Guy Demel, James Tomkins and Winston Reid are the only senior defenders available for Wednesday's FA Cup third-round replay at Manchester United.
"I've got to strengthen our defensive areas," Allardyce said. "It's less than the bare bones at the moment. It gives me great difficulty going to Old Trafford."
"What you don't want to be is like what we are, which is a little desperate because of our injury problems. At this stage of the season it's 'Call My Bluff'. You say no, they say no and then you sit and wait and bite your fingernails and hope they change their mind and say yes.
"That's why so much happens in the last week of the January transfer window. It's more expensive at this stage of January than it is at the latter stage of January."
Allardyce insisted he has not made a further bid for Blackburn's Martin Olsson, adding: "We haven't got the funds to go in with a higher bid."