The Baggies chief has endured a miserable start to life at The Hawthorns with his team having conceded 13 goals during his first four matches in charge.
Allardyce admits Albion need additions this month if they are to have a realistic chance of avoiding the drop.
But funds at The Hawthorns remain incredibly tight with all clubs feeling the pinch due to Covid-19.
Under competition rules, though, the Baggies are still able to make one domestic loan addition and two foreign loan additions this month. And that is a market Allardyce is keen to exploit.
“We’ve got three loans left,” he said.
“They won’t then commit the club to any long-term contracts.
“The owners or the board may be fearful of handing out long contracts, they might be thinking ‘what happens if we don’t stay up?’ – I understand all that.
“We talked about that before I came in.
“But what we can do is get loans or sign players on short-term contracts, players who may be out there in Europe or in this country.
“We have one loan in this country and two loans in foreign countries.
“The new rules mean that it’s more difficult than it used to be, but we must try if possible to get a better player – whatever player.
“However many players come in, they must be better than what we have and almost capable of going straight in the team immediately.
“No disrespect to my players at all, they’re trying as hard as they possibly can, but I do have to find better players to lift the squad and lift their confidence.”
Allardyce revealed he identified three players he wanted to bring to The Hawthorns but they now cannot be signed due to the tougher work permit rules imposed because of Brexit.
“The new regulations are a problem – I have found three players who are capable of coming here, but they’re not allowed,” the head coach continued.
“It’s a shame. I won’t name the players but they’d have been a big help, but due to the new regulations and the situation, in terms of a permit, they were unable to come to this country.
“Before, they could’ve done – now they can’t. Every time I’ve got to look at it and ask ‘can they qualify?’
“That’s made life more difficult for the two European or worldwide loans that we have available to us.
“It’s very difficult, but not because of the pandemic, it’s more because of the Brexit deal.”