The Black Cats, who reside at the bottom of the Premier League table, came close to grabbing all three points against City at the Etihad Stadium on Wednesday night.
Now, Liverpool are six points ahead of City, who still have a game in hand, and have a two-point lead over second-placed Chelsea.
"We are playing for ourselves - we are not playing for Liverpool," Poyet told reporters. "Maybe we helped them, and I am sure that Luis Suarez is going to be happy because there is one team less."
Sunderland are six points adrift of safety with five games left to play.