Albion climbed to fourth place in the Championship as they claimed a point at London Road, but the referee's decision not to send off Andrew Crofts for chopping down Lee Tomlin midway through the second half was the talking point.
Brighton boss Poyet said: "I can't remember the last time we had a bit of luck like that.
"There is no doubt Crofty should have been sent off but luckily for us the referee got it wrong.
"People will say that on another night the two efforts which hit the bar could well have gone in, but then again we could also have received a red card as well.
"We put in a serious performance to get what I regard as a good point at this stage of the season.
"Peterborough have beaten top teams in Cardiff and Watford recently so the first job was to be solid and keep them quiet before looking for a chance to score."