Despite travelling with confidence after a convincing 3-1 win over Liverpool, West Ham would do well to draw, he said, adding that anything more would an "outstanding" result.
               
"They will be pretty down about that performance they gave at Leicester," Allardyce told reporters.
               
"They will be hurting and they know the only way they can put that right is to get out onto the field and punish us for it - so we will have to be careful about that,” he added.
               
"A draw would be great for me. Anything more than a draw would be outstanding as far as I'm concerned,” he said.
               
Asked if it was a good time to visit Manchester, following their humiliation at Leicester where, for the first time, they lost a Premier League after leading by two goals, Allardyce said: "No. I'm thinking a backlash...
               
"I think that because of the determination of the Manchester United players and the fact they are playing at Old Trafford,” he added.
               
"I know there's quite a lot of new players playing there, but certainly the demand of Manchester United is huge and they'll be really fired up to make sure that they try and perform like they did against QPR,” he said.
               
United, under the guidance of new manager Louis van Gaal, spent 150 million pounds (USD 245 million) on new players in the transfer window, but have won only once -- 4-0 against QPR in their last home fixture -- in five league games this season.
               
They are 12th in the table, four places below West Ham, who have won twice.
               
"Hopefully, our new players won't be daunted about the prospect," added Allardyce, who said the loss of Senegal midfielder Cheikhou Kouyate for six weeks with a groin injury was "a blow".
               
West Ham will also be without captain midfielder Kevin Nolan, who has returned to training after injury.

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