The Uruguayan admits he was not expecting to be leading his side, who sit 18th in the top flight, out at Wembley so early in his tenure at the Stadium of Light.
Manchester City go into Sunday's final as strong favourites, but Sunderland have won the last two competitive meetings between the sides.
Poyet intends to enjoy every moment of the day and wants his players to do the same.
"It's going to be special. Firstly, because I was not expecting this in my first season here, and secondly because everything was very, very dark and sad when we got here," said Poyet.
"Now we are 90 minutes away - or 120 - from being the happiest people in England.
"Forget about the rest, in the cup especially, we have been a team that was difficult to play against and we have beaten top teams to have a chance to be in the final.
"Now if you asked every manager in England if they would like to be where we are, they would say to you, 'yes' because you have got a chance to win something.
"We need to make sure that we do everything possible to take this opportunity. That's the only thing I can ask of my players, everything possible."
Sunderland, who are appearing in their second League Cup final, have not lifted a major domestic trophy since beating Leeds United to win the FA Cup in 1973.
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