Adam Johnson clinched a 1-0 win in the 90th minute as the Black Cats sealed their fourth consecutive success over their bitter rivals and their third on the bounce at St James??? Park.
And Poyet was pleased to see his players finally shake off their habit of drawing as they moved four points clear of the Premier League relegation zone.
“Putting everything into consideration, we were totally deserved winners today,” Poyet told Sports.
“If you are on the losing side, it???s painful but if you look at the whole game – the clear chances we created, the way we held Newcastle and didn’t stop attacking and breaking and trying to score the goal – I think in the end it was totally deserved.
“I know sometimes a few shots and moments of noise because of this incredible stadium make it a little bit even, but overall we were much superior today.”
Poyet admitted he had almost replaced match-winner Johnson midway through the second half as he looked to break the stalemate on Tyneside.
Instead, Connor Wickham made way for Will Buckley and both Johnson and the substitute played their part in the victory for Sunderland.
“I said to the boys ‘don???t be a manager’ because in a split second, you can make a decision which goes one way or another,” he added.
“We needed someone to break and it would have involved a change of one of the two wide players. Sometimes the presence of Connor gives you something extra in the box, but Johnson???s ability gives you something also.
“I think Johnson kept himself on the pitch with a great chance which he missed but I gave him the chance to stay on. The goal shows his strength and his willingness to play and to score always here, because it’s three years in a row now that he???s scored.
“I know everybody is going to talk about Adam Johnson but it was a difficult game for Sebastian Coates to jump in, a difficult game for John O???Shea to play left-back. There were plenty of heroes today and it???s a great achievement to win four in a row against Newcastle, the biggest rivals, is great for us.”