The Black Cats defeated Manchester United 2-1 in the first leg of their semi-final at the Stadium of Light, having seen off fellow big-hitters Chelsea in the quarter-final.
Fabio Borini's 64th-minute penalty secured Sunderland's first victory over United since November 2000 after Nemanja Vidic had cancelled out Ryan Giggs' own-goal opener.
The Wearside club are now just 90 minutes away from their first major final since 1992, but Poyet admits it will be somewhat futile if they cannot retain their top-flight status, as they currently sit bottom of the table.
When asked if he could explain how Sunderland could beat the top teams, but struggles against lesser sides, he told Sky Sports: "I don't know, I am still thinking it is something very strange, we can beat the top teams but we cannot beat the ones that are down the bottom with us.
"The way we play maybe suits us when we play against the top teams, we need to change something against the others.
"If not, it is not worth it really. We want to enjoy this competition, but the Premier League is key."
Poyet admitted that there was little to choose between the two teams at the Stadium of Light, but is now keen to seize the chance of securing a trip to Wembley by holding on to their advantage in the second leg on January 22.
He added: "It was tight, I don't think one team was better than the other one, I don't think there were too many chances. A decision can go your way and you can win the game.
"It is not easy to beat Man Utd and now we have the chance to go to Old Trafford with an extra goal, so we will see.
"It would be massive (to reach the final). You don't get there too many times, it is many years from the last one, so we will try our best."