"Coming here when there is no Carroll, no Nolan, no Downing and company, then this is the game you need to win," Poyet told reporters after the game.
"Because if you come here and they are on the pitch, then it is going to be a bit more difficult. I think we did everything to win it.
"I don't like the word 'luck' but we've conceded so many own goals I was waiting for a deflected shot to go in the top corner or a bad decision from the referee to give a penalty or whatever. We need to be perfect, unfortunately, to win the game."
Sunderland still sit bottom of the Premier League with nine points after 16 games.