Bognor made the long journey to Weston-Super-Mare and exited to a fluke goal when they deserved at least another crack at the opposition.
It was another frustrating day for manager Jack Pearce as the Rocks failed to make the most of their superiority once again.
He said: "I can't believe how often we can dominate teams and not get any rewards.
"At the moment we need to sharpen up as a team in front of goal and that includes everybody not just the strikers."
The Seagulls had the better chances in the opening 45 minutes until Bognor found their feet near half time.
Bognor stepped up a gear in the second period, only for their play in the final third to let them down.
Bognor immediately found themselves on the back foot and with just ten minutes gone were a goal behind.
Matthew Rose was allowed to cross from the left and his effort took a deflection via a divot in front of Craig Stoner to bounce up and over the keeper. Despite the attempts of David Birmingham, the ball somehow managed to squeeze in at the far post off the defender's legs.
Rose could have extended the lead within a minute only to be denied by a splendid save from Stoner who then tipped Justin Skinner's header onto the bar.
A poor backpass from Birmingham let Stuart Slater in only for the former West Ham player to be denied by a fine sliding tackle in the box by Kevin Murphy.
Minutes later Murphy came agonisingly close to scoring for the Rocks but his header from a David Piper cross inched past the far post as Bognor began to dominate.
The start of the second period saw Matt Russell denied by Stuart Jones who tipped his close- range header over the top.
Lee Jarman then saw a powerful header from a corner cleared off his own line by Piper as the home side looked to catch the Rocks on the counter attack.
Russell was unlucky with an effort from the edge of the box which he curled narrowly past the far post before Slater was denied by a fine save from Stoner late in the game.
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