The result leaves Sunderland rock bottom of the table, seven points from safety, and Poyet acknowledged that his side would need to pull off something special to stay up.
"I think the desire is there but we are missing a few things that are very important in football, the quality in certain moments be it scoring a goal or defending," Poyet told BBC Sport.
"There are plenty of things we could improve but there is nowhere to hide, I am the manager and I take responsibility.
"Sometimes the table doesn't lie. It would be a miracle to stay up, I am realistic if we did not win a game in the last seven and now we need to win four from seven."
Things don't get any easier for Sunderland with matches against Everton, Manchester City and Chelsea in the next two weeks.