The Clarets, who had already matched the 54-point total from the 2017/18 campaign, needed a draw to set a new marker in the top flight.
However, goalkeeper Nick Pope lost out in his bid for the Golden Glove as Yves Bissouma and Aaron Connelly netted in a 2-1 win for the Seagulls.
Chris Wood had levelled for the home side just before the break while Jay Rodriguez saw his second half header chalked off.
The result ended Burnley's seven-game unbeaten run on home soil as they closed the term in 10th position.
Here are the player ratings...
1. Nick Pope 6
It wasn't to be for the Burnley goalkeeper. Hernandez had a goal chalked off away at Manchester City and then Bissouma opened the scoring a Turf Moor with a stunning finish. Could have done more to keep out Connelly's finish.
2. Phil Bardsley 6
Not directly culpable, but both Brighton goals came down that side. Switched off for a short corner that led to the first and failed to get to the ball ahead of Connelly in the build up to the second. Did well, otherwise, as Brighton looked to overload.
3. James Tarkowski 7
A model of consistency at the back for Burnley. Made a couple of perfectly-timed tackles inside the penalty area in the first half and was solid in the second. Could possibly have done better to cut out Maupay's pass for Connelly's winner.
4. Kevin Long 5
Beaten to a Lamptey cross in the first half when Maupay headed against the bar and was then caught out for pace by Connelly in the second as the Irishman cut in from the left to restore Brighton's lead. Had a big chance to equalise and make amends.