The Wearside club secured their first away victory in the top flight this season on Monday, but it could have been very different had referee Phil Dowd awarded a penalty inside 30 seconds.
Former Sunderland striker Fraizer Campbell was caught by Santiago Vergini as he raced through on goal, but Dowd waved play on.
Steven Fletcher put the visitors in front with a first-half header, then struck again in time added on at Selhurst Park to seal the points after Jordi Gomez had restored Sunderland's lead following a Wes Brown own goal.
Poyet's side had suffered a humiliating 8-0 hammering at Southampton in their previous away game, then lost 2-0 at home to Arsenal last weekend.
Head coach Poyet admitted Palace were unfortunate not to be awarded a spot-kick, but the Uruguayan was happy to benefit from the London club's misfortune.
He told Sky Sports: "I didn't know if it was [a penalty] at the time, but after seeing [Palace manager] Mr [Neil] Warnock talking to people and information from the top saying it was, I was thinking maybe we got lucky for once. It was time."
He added: "It means a lot [to win], it means more than what anyone can think.
"It's been a difficult couple of weeks, it looked like what we did at the beginning of the season had been thrown away."
Poyet dropped Fletcher from his squad earlier in the season and has been impressed with the reaction showed by the Scotland striker.
He said: "Fletch has been outstanding after that little spell out of the team.
"He came back really strong, showing why he is so important for us. Not just [against Palace], it's every day in training."
Sunderland revealed that defender Patrick van Aanholt suffered a suspected dislocated shoulder in a challenge with Wilfried Zaha, which Palace also felt should have resulted in a penalty.
