The Seagulls were the better side for the first half of Friday's match at Selhurst Park but had to defend solidly in the second to claim a clean sheet.
Dean Hammond had the best chance of the game for the away side before the break but home keeper Julian Speroni produced a superb reflex save to palm away the midfielder's close-range header.
"We are at home, so I'll put it at 55 or maybe 60/40 in our favour for sure," said Poyet.
"It is a final. We are playing at home and we need to take make that home advantage count.
"We need to be pleased. We are a difficult team to beat and I am very happy.
"I think it was clear that for a half we were the better team. I thought we were technically very good and controlled it.
"As you would imagine we expected a big change from Palace in the second half and that happened so it was more crazy and a bit more open. Those are the games that are difficult to defend.
"If you'd asked me before the whole 47 games before today that we would have the opportunity to go into the play-off final playing at home with a 0-0 I would take it."
Brighton have lost just three times at home in the league this season, conceding only 17 goals.