Will Buckley grabbed a first half brace for the Seagulls, while Simon Church netted a last-gasp consolation for the hosts.
And Poyet enthused: "Three hours ago we were one win in nine and people were saying that was terrible.
"Now they are saying we are unbeaten in five and it's fantastic. We are a good team and difficult to play against. I am happy for the players.
"Sometimes football is fair and you get three points but other times you have to take it on the chin and go home.
"We have had to battle and some of our players are not used to that type of football. It's a learning curve."