"I'm very pleased with the character we showed today because we defended very well right until the end," Poyet told the club's official website.
"We were playing against a good Portsmouth side but we kept playing football, we kept our identity as a football club and we showed great strength.
"We did get a bit lucky at the end because we got away with a late penalty but sometimes you need a bit of luck. I believe we deserved the points."
Brighton have taken maximum points from their two opening Championship fixtures, having defeated Doncaster Rovers 2-1 last weekend.