The Reds went down to a humiliating 5-1 loss on the south coast in August, but they gained revenge on home soil with three points which put another dent in the Seagulls' stuttering play-off hopes
Jason Scotland and Chris Dagnall scored either side of Leonardo Ulloa's leveller, though the Brighton's striker night ended in misery when he saw Luke Steele save a late penalty.
"I was convinced we had a great chance and I believe we lost the chance of getting three points," Poyet said.
"We knew we would have to fight and compete and I got the feeling that we gave the game away with the goals that we gave away, but that is how it has been for a while so I am not surprised.
"Unfortunately I am getting used to this, we have played three games away from home in a week. The first game was terrible, then we were by far the better team at Bolton and lost 1-0 and here if anyone said Barnsley deserved to win then I should retire.
"The good thing is the only people to blame is ourselves. It's not the opposition, the pitch, the referee or the weather. We have another nine games and we'll see. We'll try our best."