Depleted Billingshurst missed a chance to earn a point at Sidlesham.
Darren Annis fluffed his shot from a penalty kick in the closing stages.
The home side took the lead in the 65th minute through a goal by Sidlesham’s Tom Kelly.
Billingshurst were without four regular starters plus both manager Mark Betts who was away on a ski holiday and his assistant due to a tree falling on his van during the storm.
This left coach Steve Sale to take charge alongside chairman Kevin Tilley.
New striker James Morey impressed on his debut, putting a chance narrowly wide.
Also, Chris Osborne was denied a headed goal by Sidlesham’s alert keeper Carl Rogers.