The Seagulls currently occupy the final play-off spot, a point behind Nottingham Forest in fifth and two ahead of nearest challengers Leicester and Bolton.
Poyet has set his side a target of three wins from their final five matches, starting at Middlesbrough next weekend.
"This race for the play-offs will go to the last game," he said.
"We have plenty of games to come and everyone that's involved have got to play each other so it will be close.
"Everybody is giving each other chances but it's still in our hands and it's up to us to make more points than Leicester and Bolton."