Andy Scott's men had the better of the chances in a keenly-fought contest but neither side's strikers were able to make the vital breakthrough.
Home substitute Marcus Bean came closest to scoring in the dying minutes when he got on the end of a Cleveland Taylor cross, only to see Albion keeper Michel Kuipers equal to it with a fine block.
Anything other than a point would have been harsh on the visitors, though, who tested Bees keeper Lewis Price with efforts from Alan Navarro and Mark Wright.
Brighton midfielder Kevin McLeod also flashed a shot just wide in the opening half before Brentford came into the game after the break.
Bees striker Myles Weston fired narrowly over before Taylor saw a low shot blocked at the near post.