Allardyce is preparing his charges for a visit to Old Trafford, fresh off the back of a 2-1 victory at Tottenham in the League Cup on Wednesday.
David Moyes' men have lost three home matches in the Premier League this term, including back-to-back 1-0 defeats to Everton and Newcastle United in their previous two outings on home turf.
The reigning champions have not lost three successive home league encounters since the 1978-79 season.
But Allardyce warned his squad that United will be desperate to avoid defeat, and called for the side to match the hosts' intensity and end a three-match winless run in the top flight.
"Looking back at Manchester United's history when was the last time that Manchester United lost three home games on the trot?" he said.
"What will the odds be for that? It's not what Manchester United or David Moyes wants to do or the players in fact. On that basis, knowing Manchester United players, their desire and determination to win that game will be greater against us.
"That will focus them even more and make sure that when they come off they've beat us. We have to make sure we match their desire and determination and the tactical organisation we showed against Tottenham.
"The key element will be, if you get a chance try and score, see if there's any frailties that may come out in Manchester United.
"I expect a tough match and I expect Manchester United to make sure they go all out to win. In our position I expect us to go and play our best within the tactical structure that we need to."
Midfielder Ravel Morrison could be set to feature against his former club, and Allardyce warned the 20-year-old not to play as an individual.
"He probably would (have a point to prove) if selected," Allardyce continued. "My concern is that if he is going to play, if I do select him, then don't try and win the game by yourself.
"This is a team game and if you want to win it play as a team, not as an individual."
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