Just a week after losing 3-1 to Manchester City in the final of the Capital One Cup, the Black Cats missed out on a second trip to Wembley after suffering a third defeat by Hull this season.
Goals from Curtis Davies, David Meyler and Matty Fryatt in the space of nine second-half minutes secured a semi-final spot for Hull, who also saw Sone Aluko's first-half penalty saved by Oscar Ustari.
Poyet made six changes to his starting line-up from last week and watched the Black Cats struggle to create any chances of note at the KC Stadium.
The Sunderland boss said: "We didn't create enough but I'm not going to try to find any excuses.
"The players who played today were not good enough and that is simple - in the 50-50s, in the diving, in dealing with the referee when he panicked for 10 minutes - in not recovering well and not creating one chance."
But Poyet refused to pin any blame on Lee Cattermole who was arguably at fault in the move which led to Meyler's second even before his back-pass howler set up Fryatt for the third goal.
Poyet added: "If you hide and you're not in the game and do nothing to take a risk, then for sure you're not going to make any (mistakes).
"That's the bad side of football - the ones that take responsibility and the ones that care, they are the ones who are in the position to make the mistakes - that's football."