"They have helped us get there but everybody is fit and I am only allowed to take a certain number of players, so it's going to be hard for a few."
Sunderland, who were runners up in the League Cup in 1985, have not won a major trophy since lifting the FA Cup in 1973.
Uruguayan Poyet, who has been in charge of Sunderland since October, will be without injured goalkeeper Keiren Westwood and cup-tied midfielder Liam Bridcutt for the club's first major final since 1992.
"Apart from Westy (Westwood), which is a long-term injury, every single player is fit - even the ones who are not available, like Liam (Bridcutt) who is cup-tied," said Poyet, who will have defender Wes Brown available after suspension.
"This week, everybody's there. If nothing happens, there's going to be a big decision for me and, I hope, big understanding from the players."
(Reporting By Michael Hann; editing by Toby Davis)
