The home side had the better of the few clear-cut chances created but this was perhaps the most forgettable match of the season at Bloomfield Road.
Simon Grayson named an unchanged side, with Michael Jackson yet to fully recover from the illness which forced his last-minute withdrawal against Bournemouth in midweek.
It was virtually half-time before the first goalmouth incident of note, Claus Jorgensen heading wide from close range.
The best chances continue to fall to the midfielder, who was denied by keeper Scott Flinders late on.
The Seagulls rarely threatened, though Jake Robinson did force one fine save from Paul Rachubka.
However, the point was enough to move Pool up to sixth place on goal difference thanks to Tranmere's defeat by Swansea.
Blackpool: Rachubka, Barker, Evatt, Gorkss, Coid, Forbes, Jorgensen, Fox, Gillett, Morrell, Burgess. Subs: Evans, Parker, Vernon, Joseph, Hoolahan.
Brighton: Flinders, El-Abd, Lynch, Butters, Mayo, Cox, Bertin, Robinson, Hammond, Revell, Savage. Subs: Kuipers, Ward, Hart, Elder, O'Cearuill. Referee: A Taylor (Cheshire)