"If somebody needs to win, then of course it's Manchester United. Everybody in the world will be expecting them to win, but because of that, there's more pressure on them," Poyet is quoted as saying by The Mirror.
"It could be a must-win for them because it's a possibility to win a trophy, it's a possibility of beating their biggest rivals Manchester City [in the final] to win a trophy. It's an important game for Manchester United, for sure."
Poyet also feels that Moyes took on the hardest job in world football when he replaced Sir Alex Ferguson.
"David took the most difficult job in the world after Sir Alex left," he added.
"It was always going to be the most difficult job in the world. It's a big change, and it's not like when you change managers at any other club, after two or three years. I hope he's given time to change things round because he deserves that for what he's done at Everton."
Manchester City await the winners in the final.