Blues' hopes of completing the double were boosted when captain Steven Caldwell scored with a glancing header from a Rob Hall corner in the 17th minute.
But Brighton's eager play enabled them to dominate the midfield and they broke away for Ashley Barnes to notch his sixth goal of the season following a left-wing cross from Andrea Orlandi.
The best goal of the game was a sweet cross-shot on the volley from David Lopez which whistled past Jack Butland to put Brighton 2-1 ahead in the 43rd minute.
But with time running out Nikola Zigic produced a face-saving goal, to the embarrassment of Seagulls goalkeeper Tomasz Kuszczak.
Poyet said: "The best thing that occurred early on was to concede a goal. We were sloppy and not playing at the tempo I like.
"After that goal we were a good team to watch and we created problems until the 92nd minute when Birmingham equalised. The last four minutes contained the mistake by my goalkeeper and a brilliant save from Butland.
"We scored two very good goals and the bonus for us was Ashley Barnes. He works well everywhere. We dropped two points against Birmingham and we only have ourselves to blame.
"It was really sad to see Tomasz Kuszczak make one mistake. It was terrible. Let us hope it is a one-off. He is devastated. I know Tomasz from last year and he has not made one mistake.
"But I am now going to learn from his reaction from the next game. So Tuesday [when Brighton play Blackburn] will be a good learning situation for myself."
- Sports & Recreation