The Hawks went down 1-0 to Tonbridge Angels in the Blue Square Bet South.
Lee Bradbury’s men lost to a disputed first-half penalty given against Ed Harris.
Meanwhile in the Russell-Cotes Cup, Gosport beat Locks Heath 2-1 and Fareham recorded a stunning 4-3 success over Moneyfields at Dover Road.
Graham Lindsey held his nerve from the penalty spot in the final minute of extra-time to send Fareham through.
In the Wessex League premier division, AFC Portchester lost 3-1 to Newport IOW at Wicor Rec.