The Black Cats boss says a win in the Tyne-Wear derby is the top of fans' wish lists.
The Uruguayan was speaking at a pre-match press conference ahead of Sunderland's Premier League clash with Stoke City this weekend and revealed fans always ask him the same things.
One is to win a cup - but the most important is to 'beat Newcastle.'
The Magpies currently find themselves in 10th in the league table, although Sunderland are just two points - and places - above in 17th.
"It doesn't matter how young a kid or how old in Sunderland, if they see me they know who I am and they always speak to you," Poyet told reporters.
"They ask you to beat Newcastle and they ask you to win a cup and that is because that is what they are living for.
"I like that pressure because it is up to me, how I train, how I do things and how I put the team on the pitch.
"It is an extra pressure on the players so you have to be strong to be here. It is not easy, especially for players who are coming from places that do not have the same characteristics as the North-East, even in the weather. It is special."