The Seagulls endured a miserable Saturday afternoon at Hillsborough, losing striker Ashley Barnes to an early red card and conceding a third goal moments after they had dragged themselves back into the game through Andrea Orlandi.
But Poyet, whose side face more Yorkshire opposition in the shape of Hull next weekend, insisted: "We played better than people think.
"Everyone will look at the scoreline and then watch the goals on the highlights, but we were better than that.
"But there are key moments in a game and that moment was the sending-off and the goal that followed from the resulting free-kick. It was one of the worst goals we have conceded this season which is very disappointing."