However, Poyet feels that things could have turned out differently had referee Howard Webb awarded them a spot-kick when, with the scores at 1-0, Nolan appeared to control the ball with his hand inside the box.
"It was clear, deliberate. He tried to play the ball with his hand," he told Sky Sports News.
"You would need to ask the referee. It was easy to see but that's the way it's been. I hope we get some luck; a decision from the ref or a deflected shot goes in.
"It's about winning now. We have a chance and will go to the end."
The result left relegation-threatened Sunderland winless in seven matches, and four points adrift of safety.