The manager underlined the strength of the champions' squad ahead of their tip to Upton Park, but backed Andy Carroll to make the difference after scoring last weekend
It will be a second game in four days for David Moyes' men following their stirring comeback to see off Olympiakos in the Champions League last 16 on Wednesday.
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"David's got so many players to choose from that fatigue won't come in to it for them," he told the club's official website.. "We'll have to be at the top of our form."
Allardyce also showed his support for Moyes, who has come under fire after a disappointing first season at Old Trafford.
"Transition is a big thing," he added. "When one of the greatest managers in the world leaves, transition is a big thing.
"When someone else comes in they have to be given time to make the changes they need to do."
Allardyce saw a return to the scoresheet for Andy Carroll last week, but ultimately the striker's goal counted for little as Stoke City came back to win 3-1 at the Britannia Stadium.
The manager hoped it would be the first of many for Carroll between now and the end of the season, with West Ham still not safe from relegation.
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"We don't put any great value in the table because our aim is always to obtain more points than games played.
"We know full well that we've got a little bit more to do. I think probably about 38 points will keep you up but there's still 10 teams in it."