Albion battled to a goalless draw in Friday's first leg at Selhurst Park and are now favourites to progress to Wembley.
"We've got massive confidence going into the next game," said Bridcutt. "The Amex is our home ground and we've made it a fortress really.
"We will go out and play the football we know we can play and enjoy the occasion.
"We knew from the start it would be tough for us on Friday. There was a bit more added pressure - it's a local rivalry and it's about who gets to the final, but we handled it well and showed our character.
"In the first half we dominated the game and in the second half they made it a lot harder for us but we knew that would happen, we knew they would get a lot of the ball at one stage of the game but we handled it well and kept a clean sheet.
"We go into every game looking to win, that's our mentality, but to get a draw was great."
Brighton manager Gus Poyet added: "We have a great opportunity. It won't be easy and of course we need to make home advantage count. I'm sure at home, in front of our fans, it will be a little bit easier for us to create something."