In-form striker Matt Derbyshire put Nottingham Forest in front but Stephen Ward and a late Leo Ulloa goal gave the Seagulls victory.
With Reading held at home by Burnley it means Brighton take the last top-six spot on a total of 72 points.
The Reds finish 11th on 65 points but caretaker manager Gary Brazil gave the thumbs-up afterwards to the incoming arrival of Stuart Pearce as manager.
He told the official NFFC website: “That’s going to instill a lot of energy in this place. We need to dust ourselves down and look forward to the new season.”