The Hammers put in arguably their worst performance of the season at the weekend when they were outclassed by Spurs, who ran out 3-1 winners at White Hart Lane. Tonight West Ham face an even harder test when they travel to Old Trafford - where they have won three of their last 21 visits - in the second of a difficult run of fixtures. But Allardyce was encouraged by recent performances when his team were underdogs and he hopes his men can pull off a shock result in his home county of Lancashire this evening.
"The team did brilliantly when we drew against Manchester City and beat Newcastle so let's see if they can do it against Manchester United, Chelsea, West Brom or Liverpool," Allardyce said.
"There is no real pressure on the lads. It's a match they will enjoy. It's a game they will have dreamed about since they were kids.
"If we give a good account of ourselves then hopefully it will be good enough to get us something from the game." Allardyce has developed a close friendship with Red Devils manager Sir Alex Ferguson over the years, and he fully expects to be invited in to the Scot's office after the match for his customary glass of red wine. Whether Allardyce will be toasting a Hammers win will depend a lot on luck, the 58-year-old admits.
"Historically you've got to be one of the lucky ones when you go to Old Trafford and win," Allardyce said.
"If you look at their track record at home they only lose once or twice all season. If you're going to win at Old Trafford - if it's your time and your turn - it has to be a moment where your team plays in every position to its best and takes advantage of a below-par Manchester United."
Unfortunately for Allardyce he will tonight be without key midfielder Mark Noble, who is suspended after accumulating five yellow cards this term. Left-back George McCartney will today have a fitness test to see if he has overcome the ankle injury he sustained in the defeat at White Hart Lane.