The Hawks crashed out of the FA Cup after losing 3-2 against Weston-super-Mare in their third qualifying round tie at Woodspring Stadium.
Steve Ramsey gave the Hawks a dream start after three minutes from the penalty spot.
But the Seagulls hit back with two goals, before Ollie Palmer levelled things up on the stroke of half-time.
The Seagulls grabbed the decisive goal early in the second half, capitalising on a slip in the visitors defence.
Ex-Pompey striker Vincent Pericard was absent from the Hawks squad after deciding not to cup-tie himself.
Former Hawk Tony Taggart bagged two goals as Blue Square Bet South side Sutton proved too strong for Bognor in a 4-0 loss.
After being part of the Hawks team who played Liverpool in 2008, Taggart hit a double as the Rocks were overpowered.