Sebastian Larsson's first-half winner secured victory for Sunderland and gave them a great chance of avoiding relegation from the Premier League.
After the game, Poyet told reporters: "I said a long time ago that we would fight to the end, and what a game of football we played today.
"I don't know how many records have changed this season, we have been down there all season but if we win and stay up it's an incredible season. We done so many things right but it's been so difficult.
"I hope my old team Chelsea give me a hand tomorrow. But if we win one more game we are safe. I said to the boys after the game, thank you. It was tough and there were moments when we looked very tired but we coped with the situation and the clean sheet today is immense."
Sunderland take on West Bromwich Albion in their next league game.