Vicky Jepson’s side, including debutant Rachel Furness, were on the front foot during the opening 45 minutes and went closest to breaking the deadlock midway through the half.
Rinsola Babajide, leading the line for the Reds, stole possession in the opposition box and sent in a strike that was inches wide of the post.
But instead it was Brighton who produced what proved to be the decisive goal shortly after the half-hour mark.
A deep, hanging cross from the left touchline was turned back into the middle of the Liverpool area and Aileen Whelan nudged a finish past Frances Kitching.