Papiss Cisse and Fabricio Coloccini were missing with respective thigh and hamstring injuries for the Magpies. The influential Hatem Ben Arfa, Yohan Cabaye and Steven Taylor are out until next month, Cheick Tiote has been lost to the African Nations Cup and Demba Ba was sold to Chelsea.
But for the second successive year, Brighton dumped Newcastle out of the competition with goals from Andrea Orlandi and Will Hoskins humbling their Premier League opponents.
"We had a great opportunity because of the players that were missing to beat a Premier League team. What a team you could make up of the players they had missing," Poyet said.
"But it was more up to us than the opposition. We deserve it because of the way we played. We were the better team."
Orlandi's opener was exceptional with the Spaniard capitalising on Wayne Bridge's determination in chasing down a seemingly lost cause by producing an exquisite touch, turn and shot.
"Andrea's finish by itself was enough for people who paid for a ticket. That was perfection," Poyet said.
"You don't see it week-in week-out anywhere. You want to see something different and that was spectacular. The timing of the goal was good."