The Seagulls held Ian holloway's side to a goalless stalemate at Selhurst Park on Friday night with the second leg to come back in Brighton on Monday.
Bridcutt hailed a 'massive result' as the Seagulls attempt to win through to the Wembley final against either Leicester or Watford.
He told Sky Sports: "It's a massive result for us. Teams come here and get turned over quite easily and we have played well at times and now we have to go back to our home ground and we've got an advantage now.
"It's been a long week building up to the game and we're just looking forward to taking the game back home and going for the win."