The 66-year-old's disappointing start to life as Baggies boss continued on Saturday after his side were dumped out the FA Cup on penalties by League One Blackpool.
It means Allardyce has lost four of his opening five matches in charge – with the only exception a draw achieved at Liverpool.
Allardyce has already bolstered his squad by signing midfielder Robert Snodgrass and back-up goalkeeper Andy Lonergan this month.
As a bare minimum, he also wants to sign a defender, striker and defensive midfielder – with talks ongoing with Leicester over a move for Hamza Choudhury.
But he concedes Albion's hopes of Premier League survival look to rest on the extra additions he can make in the coming weeks.
"I'm hoping to be extremely busy in the window," Allardyce said.
"It's part of the process to work tirelessly on outs and ins until the end of January.
"Everybody knows what we need to do. We need to move players in this window. We need to bring players in.
"Everybody needs players but I think more than anybody in the Premier League we need players to give us a chance of moving out of the position we're in."
Reports have linked Albion with a move for Bournemouth's Josh King this month – although it seems unlikely the Baggies would be able to afford the striker with Everton keen.
And when asked about the Norwegian, Allardyce admitted he was unsure if Albion would be able to strike a deal for the 28-year-old.
"I don’t know – I have no idea what the cost or price will be," the boss when asked if he is keen on King.
"If the price is within our range then I think we would be interested. If it is out of our price range we won’t be interested."
In a bid to free up funds for wages, Albion have allowed Charlie Austin to leave the club on loan – with the 31-year-old having returned to former club QPR.
“I’d like to thank Charlie for his dedication and professionalism during his season and a half with us," said Albion's technical director Luke Dowling.
“Many of his goals for us proved to be crucial and I don’t think any Albion fan who was at St Andrew’s will forget his performance against Birmingham City to earn us a valuable win at what was a pivotal point in our season.
“Everyone at the training ground will miss Charlie’s presence and we all wish him well in his future career.”
Meanwhile, third-choice Albion goalkeeper Jonathan Bond is believed to closing in on a move to LA Galaxy.