Michel Kuipers produced some inspired saves as Brighton virtually ended Forest's hopes of automatic promotion.
The Albion keeper's best stop came when Kris Commons evaded three challenges but saw his shot pushed away.
Forest's Nathan Tyson went close with a header and Matt Thornhill also missed a good chance to put the home side ahead.
At the other end, Brighton striker Nicky Forster missed an open goal before Forest keeper Paul Smith pushed Tommy Elphick's header onto the bar.
Nottm Forest: Smith, Chambers (McCleary 73), Morgan, Wilson, Bennett, Clingan, Thornhill (McGugan 73), Cohen (Agogo 84), Commons, Tyson, Ormerod.Subs Not Used: Sinclair, Byrne.
Booked: Cohen.
Brighton: Kuipers, Hart, Elphick, Lynch, Mayo, Martot, Thomson (Loft 69), Racon, Cox (Butters 90), Murray, Forster (Robinson 74).Subs Not Used: Gatting, McFaul.
Booked: Hart, Thomson.
Att: 18,165
Ref: Nigel Miller (Durham).
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