Poyet laments Sunderland mistakes
Adam Johnson gave Sunderland the lead just 29 seconds in at the Stadium of Light, but poor defending allowed Hull forward Gaston Ramirez space to unleash a 32nd-minute shot, which took an unusual bobble and beat goalkeeper Costel Pantilimon.
Sunderland were denied what appeared a clear-cut penalty for an Alex Bruce handball just before the break, and early in the second half James Chester was left unmarked to head Hull in front.
Nikica Jelavic sealed victory with a goal on the counter-attack in stoppage time.
"The first two goals were not something you regularly see," said Poyet. "The first one found Johnno chasing and he got his reward with the goal, and then the second saw an incredible bounce beat the keeper.
"After that I think the game was pretty equal. We weren't fantastic, but we were in the game and we needed to pick our moments.
"I was disappointed with the penalty decision, I thought it was clear-cut but it was not given.
"There were lots of emotions running throughout the game and after the incidents we had a number of half-chances right at the end of the first half, and that seemed to change the atmosphere of the game.
"We conceded after we were trying to get forward and score and then we conceded from a set piece, which is not good from us. There were just too many mistakes.
"We were hurrying and trying to push forward, but we need to be better than that and be more patient with our passing.
"It was a perfect start, especially after last weekend's result. The early goal was great, but it was not to be."
The result left Sunderland 14th in the Premier League, and Poyet has urged them to beat the side directly above them next time out.
"We need to move on now, start with recovery tomorrow, and make sure we perform better on Sunday against Aston Villa," he said.