The Black Cats head for Old Trafford on Wednesday evening holding a 2-1 first leg lead in their Capital One Cup semi-final and knowing a draw will be good enough to book them a first trip to the final of a major competition at Wembley since 1992.
Poyet's men will put their Barclays Premier League woes to one side for the evening - they remain locked in a battle for survival despite their recent improvement - as they set about the task of adding to the storm clouds hanging over David Moyes' men with the defence of their title all but over, the FA Cup gone and Champions League glory looking a remote possibility.
Asked if the game is a must-win affair for United with the odds overwhelmingly in favour of derby rivals Manchester City awaiting the winners in the final, Poyet said: "Yes, it could be, it could be.
"It's a possibility to win a trophy, it's a possibility of winning a trophy by beating their biggest rivals.
"It's an important game for Manchester United, I am sure. They need to make sure that they get in there as well.
"Now, we are not going to go there feeling sorry or whatever, we are going to go there to do our job and play the game, make it difficult for them, make sure we are a difficult team to play against, that we go with the mentality to win and score goals, and then we will see.
"Then the opposition plays and if [Wayne] Rooney is available or if he is not... Like I always say, they are very, very good and they are Manchester United.
"That's no problem, we need to make sure we are good ourselves."
Both Rooney and Robin van Persie missed the first leg on Wearside through injury a fortnight ago as United slipped to one of four defeats in their last five games.
The first two of those reverses came on home turf as Tottenham and Swansea became the fourth and fifth visiting sides to win at Old Trafford this season.
As a result, a positive start by the Black Cats could adversely affect the atmosphere among the home fans, although Poyet is not counting on that.
He said: "It depends on the players on the pitch. If they are experienced players, the crowd doesn't matter too much.
"In my time, I had bad times in Spain when we didn't win games, and you need to be strong enough and have the character to play and show that it doesn't influence your game.
"If there is someone who gets influenced by the atmosphere, then he shouldn't be at Manchester United, to be honest."
Poyet will have new signings Santiago Vergini and Oscar Ustari among his squad for the first time, with defender Vergini having signed on loan for the rest of the season from Uruguayan club Atletico Fenix and keeper Ustari having signed a short-term deal after his contract at Spanish side Almeria was rescinded by mutual agreement.
He will also have striker Steven Fletcher fit to play after he found himself the subject of unflattering newspaper headlines at the weekend.
The Scotland international was used only as a substitute in Saturday's 2-2 league draw with Southampton, but Poyet insisted his absence from the team was down to injury rather than a disciplinary matter.
He said: "The injury is fine, that's the only thing I can confirm. We were very good with the way that we dealt with a little inflammation of the Achilles.
"Everything has settled. He trained yesterday and today, no problem. The Sunday news - I am not going to comment."
Asked if the striker was psychologically ready to play, Poyet said: "He looks all right. We are all different."
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