Goals from Phil Bardsley and substitute Sebastian Larsson gave Sunderland a 2-1 fourth round victory over Southampton at the Stadium of Light and set up a date with Chelsea on Wearside.
Poyet said: "I suppose that's good news, yes?
"Look, they are the games I need to enjoy. In quarter-finals, you can't ask for any small team, you know you are going to get one of the big ones.
"It's going to be special for me - an official game against Chelsea is always very special - so I am looking forward to seeing Jose and company.
"Of course, it's a cup competition, you need to win. Everybody knows a quarter-final is something we haven't achieved for many, many years, which is great for the football club.
"We are playing Chelsea, which is going to be special here at home."
Poyet insisted he never had any qualms about bringing Bardsley, who came close to leaving the club during the summer after falling out with former manager Paolo Di Canio, back into the team.
He said: "I'm not sure if it was a risk. As soon as I arrived, I saw him train. I saw how important he could be for us and the way he was training and wanting to play in friendlies behind closed doors.
"It's not something I analysed too much. He is part of the club, he is under contract and if he is good enough, he will play."