Moyes replaced Sir Alex Ferguson at Old Trafford in the summer and the reigning Barclays Premier League champions are currently eighth after losing their last two home league games.
West Ham, themselves struggling down in 17th place, visit Old Trafford on Saturday with Allardyce acknowledging the size of the job Moyes has after replacing an icon such as Ferguson.
"For him, at the moment I don't think it's quite as bad as everyone makes out," the Hammers boss said.
"(United are in the) semi-finals of the Capital One Cup, qualified (as) winners of their European group and unfortunately for him, (they are in) a league position that he wouldn't have wanted but obviously he'll face the task as he knew it was going to be a difficult takeover period from Sir Alex.
"Old Trafford particularly is where he wants it to be the fortress that Sir Alex always seemed to make it and on occasion that hasn't seemed to happen for him.
"David will be planning as always to get the right team out to beat us and go on from there. Like everybody says, the transition cannot happen overnight and it's like every manager, there's a transitional period that you've got to try and get through before you make your own mark on it."
West Ham joined United in the final four of the Capital One Cup after coming from behind to beat rivals Tottenham on Wednesday night.
A two-legged semi-final against Manchester City awaits Allardyce's side in the new year but for now the 59-year-old is keen to use the Spurs win as momentum to kick-start the Hammers' stuttering league campaign.
He said: "When you win such a game as at your local rivals, who are such a big club these days, then it does lift everybody but you must use and take that into the next game and make sure you deliver the same performance again.
"We've not won as many games as we should have done in the Premier League and that's left everybody a little down.
"Manchester United we all know, if they're on song, on top of their form on that particular day it could be very difficult for us.
"We have to go and deliver that type of performance and resilience again and be as clinical in front of goal as we were on Wednesday night, even though the opposition territorially and possession-wise were far better than we were."
Allardyce will be without skipper Kevin Nolan as he serves the final match of his three-game ban for his red card at Liverpool but former United youngster Ravel Morrison is in line for a recall to the starting line-up.
The 20-year-old left United to join West Ham in the summer of 2012 and has started making a name for himself at Upton Park, although Allardyce is keen for Saturday's game to be about more than Morrison.
When asked if the England Under-21 international may be looking to prove a point in the game, Allardyce replied: "If he is selected he probably will. My concern would be to say that if he does play and I do select him that he doesn't try and win the game by himself. This is a team game and you can't play as an individual because you're back at Old Trafford."
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- Old Trafford
- Sir Alex Ferguson
- Barclays Premier League