The hosts twice took the lead through Lawrie Wilson and then Bradley Pritchard, but goals from Craig Mackail-Smith and substitute Kazenga LuaLua secured a point for Brighton.
Poyet was satisfied with the fightback but felt that his side had been forced on the back foot by some costly errors.
"A point is all right," he said. "I'm not saying I'm happy but I will take it.
"Sometimes you need to accept that things happen for a reason, like our second goal. I was absolutely mad about how close the wall was from the wall and we scored.
"Maybe if they had moved the wall three yards back we would have hit it in the stands.
"The only problem we had was that we had to chase the game all the time. When you go down 1-0 you have to chase and you make mistakes.
"Then we scored and it looked like we had the game under control but we made a mistake and had to do it again."