Harry Kane scored a late own goal as the visitors, who had dominated possession and restricted their opponents to just one shot on target, were denied a deserved win in a 2-2 draw on Saturday.
Tottenham appeared likely victors when Christian Eriksen struck early in the second half after Adam Johnson had cancelled out Nacer Chadli's opener in the first period.
But Sunderland continued to battle away, earning a share of the spoils that left Poyet delighted.
He admitted: "That was the hardest game we have played so far and the best team we've faced. It was a really hard day and a proper point that we worked really hard to get.
"The players kept going and tried. They fought and tackled and came back into the game.
"I am sure that [Tottenham manager] Mauricio Pochettino is disappointed. But if you stay in the game, you always have a chance."
Sunderland are still yet to win in the league this season, although Poyet is keen to focus on the fact they have slipped to just one defeat in four games.
He added: "The more we talk about the win, the more difficult it will become. I could say that we have lost just one game in five.
"I just think that this was a really, really good point. If we fight the way we did here, and concentrate the way we did, then we will have a chance to get that win. That is the Premier League."
