The Cumbrians had most of the play in Saturday's League One clash at Brunton Park, but ran out of ideas after a positive start which should have had them at least a couple of goals in front.
James Berrett fired an early snap-shot inches wide then Francois Zoko's cross from the left nearly led to an own goal by Adam Al Abd.
Carlisle's slick passing had Brighton on the back foot and it took a fine diving save from Casper Ankergren to keep out Tom Taiwo's downward header after neat work by Gary Madine on the left.
Madine was next to miss out when a fraction away from making contact with Craig Curran's angled ball six yards out when any kind of touch would have been enough.
Former Carlisle striker Glenn Murray had to wait until the 66th minute for his first chance, but after eluding the home defence he slid his shot wide and Brighton showed more adventure after the break with Ashley Barnes almost snatching the win in added time when he put his close-range header straight at goalkeeper Adam Collin.