Poyet told Sky Sports News: "[This is] one of the best days I've had in football, as a manager, no doubt. Of course the three points are the most important thing.
"I don't know how many people were expecting this but I've been telling you for a few weeks that we were getting better and especially away from home we are a difficult team to play against.
"If you've got a chance like a penalty and you take it, then you become more difficulty for the home team. You need to be strong, but at the same time be relaxed to play the football that we want to play and the players they are enjoying it so all credit to the players they were outstanding today."
The win leaves Sunderland in 14th in the Premier League.