United take on Manchester City in the second leg of their Capital One Cup semi-final on Tuesday.
Ordinarily, for a team that has not won a major trophy for 24 years, a domestic semi-final would be something to shout about, but Hammers fans are bracing themselves for another hiding after they lost the first leg 6-0.
West Ham's league form is of deep concern to Allardyce, as well as the club's fans and owners, too.
The east London club slipped into the relegation zone on Saturday following a 3-1 defeat to Newcastle and Allardyce has been tossing and turning at night as he contemplates the task ahead of him.
"You lose a bit of sleep and you don't sleep quite as well as you would like to," the West Ham manager said when asked how he was coping.
"Saying that, you don't sleep much as a manager anyway."
Having been in management for 23 years, Allardyce is used to feeling the heat. He was involved in a relegation scrap while at Bolton and he also took Notts County down earlier in his career.
Neither of those clubs had a big move to the Olympic Stadium on the horizon, though.
West Ham will struggle to get anywhere near the 60,000-capacity level if they are in the second tier by the time they move there in 2016 and that is weighing heavily on Allardyce's mind.
Indeed, Allardyce reckons the pressure on him now is equal to that David Moyes is facing at Manchester United.
"People would think outside that the pressure on David is probably greater than it is on me, but from my point of view, I think it's equal - not only because of now but because of the future of this club," the 59-year-old said.
"The burden of this club is that it wants to move into the Olympic Stadium in two years' time or so and has to have a team in the Premier League to move into that stadium.
"You have to build for that, and that's a bit of extra pressure."
The main source of frustration for Allardyce, who has won one league game since the end of November, has come in the transfer market.
Allardyce conceded a deal for Lacina Traore is "dead" after the Monaco striker seemed to chose Everton over the Hammers.
Mooted moves for Johnny Heitinga, Ishak Belfodil and Joleon Lescott have not materialised.
The only players to put pen to paper at Upton Park are Wolves loanee Roger Johnson, Peterborough teenager Jaanai Gordon and Carlton Cole, who has signed a contract extension until the end of the season.
"This is mad January," Allardyce said.
"It's a lunatic transfer window that creates havoc throughout the game. To say I'm frustrated (with how the window has gone so far) would be an under-statement.
"You pass the day by not knowing how quick the time has gone.
"You get up in the morning and you come in and sometimes you think it's lunch time and it's about four o' clock and you have missed it.
"You think to yourself: 'I wondered why I was feeling so hungry!'
"You have got so many balls up in the air and in the mean time you have got to get your team out on the field playing as well."
With games against Manchester City, Tottenham, Manchester United, Arsenal and Liverpool in their final eight matches, Allardyce knows his team must start winning games fast.
The good news for the Hammers boss is that Andy Carroll has reacted well to his introduction back into the first team.
Carroll has come off the bench for West Ham in the last two games following an eight-month spell on the sidelines and he will feature against City on Tuesday.
Allardyce confirmed that Ravel Morrison will play and that Ricardo Vaz Te is fit again after three months out with a shoulder injury.
A place in the final is surely beyond West Ham, but Allardyce wants to see some fight from his players against Manuel Pellegrini's side.
"It's highly unlikely we will get through," Allardyce said.
"But we are at home, we are playing for pride and will try to play well and get a result."