For Gus Poyet's men it's a third game without a victory following their five-match winning streak which had seen them lead the way in the Championship during September.
But aside from a 20-minute period after the interval where Brighton had a series of good chances, they were unable to find the net as they badly missed injured top scorer Craig Mackail-Smith.
The home side struggled to break down a stubborn Albion backline who have now conceded just three times in five away league games this season, this despite having nine corners in the game.
Brighton looked a real threat early on with their patient passing game, but the best they could manage was Andrea Orlandi trying his luck twice from distance.
The first goalkeeper to be called into action was Derby's Adam Legzdins, who had to be alert to save David Lopez's free-kick which he managed to get up and over the wall and saw it bounce awkwardly in front of the Rams shot stopper.
Derby struggled to get a foothold in the game in the opening quarter and their first shot only came on 21 minutes when Paul Coutts dragged a right-foot shot wide from 20 yards out.
Orlandi then headed over the crossbar at the far post after a deep cross, before the visitors were forced to make a change as Tuesday night's late goal hero in the 1-1 draw against Ipswich, Will Buckley, hobbled off injured to be replaced by Stephen Dobbie - who struck an effort wide just before the break after a flowing move.
After a disappointing first half, Albion hit the crossbar minutes after the restart when Liam Bridcutt's left-foot shot from the edge of the area took a deflection and had Legzdins rooted to the spot as it came back off the woodwork.
The Rams defence then backed off to allow Dobbie the chance to turn just outside the area and send his shot just over the bar.
The visitors were doing all the pressing at the start of the second half as they bossed possession and Lopez was next to go close but steered just wide of the left post after a neat lay-off by Dobbie.
Brighton were the team looking most likely to break the deadlock and Gary Dicker's inswinging corner from the left was met by the head of substitute Dean Hammond but Legzdins parried away before Gordon Greer headed the rebound wide from six yards out.
This seemed to wake the hosts, who up to this point had barely had a shot on goal but then forced Brighton goalkeeper Tomasz Kuszczak into two fine saves in a matter of a minute - the Pole tipping shots from distance by John Brayford and then Craig Bryson behind for corners.
Both teams endeavoured to find a late winner and the home side enjoyed a five-minute period of pressure without ever further troubling Kuszczak as the game ended without a goal being scored.