The win took Sunderland out of the bottom three.
Poyet said: "It means a lot - more than anyone can think.
"The idea was to come back, somehow (from the recent defeats). It's not always about playing nice - it's doing the basics. The best part was the goals - you don't score too many away from goals the way we did today."
It could have worked out differently had Palace been given a penalty inside the first 30 seconds when Santiago Vergini felled Fraizer Campbell in the box.
Referencing the penalty appeal, Poyet said: "I didn't know if it was but, after seeing Mr Warnock talking to people and the information coming from the top, it was.
"It's time we maybe got a bit of luck. It was a difficult time for the referee."
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