Manchester United stand between the Black Cats and a first trip to a major final since 1992 - and their first in the League Cup since 1985 - when the sides meet at Old Trafford on Wednesday evening.
They will do so with Poyet's men holding a 2-1 first leg lead and with the likes of United old boys John O'Shea and Wes Brown, as well as Sebastian Larsson, Craig Gardner and Ki Sung-yueng, knowing exactly what it takes to win the competition.
However, many of their team-mates have never reached a major final, and the Uruguayan knows chances to do so do not come around too often for all but the biggest clubs.
Poyet, whose side will be roared on by 9,000 expectant travelling fans, said: "I always say that.
"There are plenty who have never had this opportunity, either because they are too young or because they have been playing in teams that didn't have the chance to reach this possibility.
"That's why we need to make sure that we do everything possible to give those players the chance to feel what it means to play in a final at Wembley and have the opportunity of winning a trophy.
"People think it's easy to get to a semi-final and a final, but you don't get it every year and that shows you how difficult it is, apart from the top teams who normally are close.
"It's a great opportunity."
To that end, Poyet will send his players out under instructions to seal their own destiny by taking the game to United rather than attempting to edge their way to Wembley.
He said: "The important thing is we need to score. If we go there thinking that the only way to get through is getting a 0-0, we are wrong.
"We need to try to score and play the game and manage the game."
Poyet will have two new faces in his squad with Argentinians Santiago Vergini and Oscar Ustari having joined the club this week.
Goalkeeper Ustari is likely to be named among the substitutes, while Vergini may have to be a little more patient, although Poyet, who revealed he had been tracking the defender for 18 months, is hopeful he will make an impact on Wearside.
He said: "He's going to bring experience, a winning mentality - he won the league in Argentina and he has started going with the national team, even if he has played only one game.
"He's a good character, a proper Argentinian defender I can call him. He is big, which is good for England, and he can pass the ball, so he has got everything to be a success in England.
"Then it will depend on the way we play, how he adapts and then to see if the football in reality is good for him. But I think he could be great for us."