The Seagulls grabbed a gutsy goalless draw in Friday's first leg in south London and are favourites to progress to Wembley.
"We've got massive confidence going into the next game," admitted midfielder 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."
Midfielder Bridcutt was his usual composed self as Brighton dominated the first half at Selhurst Park before Palace came back strongly after the break.
The 23-year-old former Chelsea trainee added: "We knew from the start it would be tough for us. 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."
Bridcutt had sympathy for former Seagulls team-mate Glenn Murray, Palace's 30-goal top scorer, who will miss out on a return to the south coast after suffering a suspected cruciate injury in the second half.
"It looked really bad," said Bridcutt. "As a footballer you hate to see people get injured, obviously with Glenn he's a close friend of ours and we wish him a speedy recovery."
Unlike Palace, Brighton came through the first leg unscathed but manager Gus Poyet may rotate his squad.
"We'll see how the players react and we'll see if there are any problems because we might have to freshen up the team," he said. "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."
- Sports & Recreation