The Seagulls appeared set for three points at Molineux, where Wolves had been reduced to 10 men, but Roger Johnson popped up in the last minute to earn the home side a point.
Brighton had trailed twice, despite Wolves having Karl Henry sent off for an ugly lunge on Liam Bridcutt, and Poyet said: "I hate these situations because we are better than that. It is not good enough.
"The good thing, if you can see a good thing, is that it is only us to blame. We cannot blame anyone else. So we have to take it on the chin, go back and try to be normal next week.
"We have been very good at defending until last Friday (a 2-2 draw against Leeds United), we always conceded a maximum of one goal per game.
"Then in that crazy game against Leeds we conceded two and against Wolves we have conceded three for the first time and we gave it to Wolves.
"I give credit to the first goal, was it was a good one-two and a good finish. But the other two is not us and that is basic. They are things you need to do every day whether you are training or playing.
"We do it well but we didn't do it against Wolves. The other side of the game, that is us. We created 10 or 15 chances against a team with 10 men, that is normal. If we didn't do that then I would probably be resigning!
"But you need to do the basics and we didn't do it, and that made me feel really bad today."