Phil Bardsley's first-half strike proved to be the difference between the two sides as Poyet made it three home wins from three since taking charge at the Stadium of Light.
Prior to his arrival, the Black Cats had been without a Premier League win all season, but the former Chelsea star was quick to put the turn in fortunes down to the efforts of his players
"They deserve all the credit - they're the ones we had on the pitch," he told Sky Sports.
"We can plan, we can talk, we train, but at the end of the day, it's the players that are on the pitch and they need to do it.
"They were outstanding. Tactically, it was difficult to play but we took a lot. We tried to plan the game in three days and tried to convince them that it was possible.
"Especially to keep a clean sheet against a top, top team. It shows that we believe."
Poyet also saluted returning defender Wes Brown, with the former Manchester United man earning the Man of the Match award on his first league start in 22 months.
"Credit to him, credit to Wes. I was thinking to put him in straight away as soon as I arrived at the club but for some reason we thought that he was still a few weeks away from it," he said.
"Then he put himself in the under-21s for a couple of games, then he needed to jump in the 9 v 11 game (against Hull City), then the cup game in the middle was practically perfect for him to be in a better condition.
"Now it's about giving him a couple of days rest to recover. I think it's easier to recover when you win games."