Charncey Dash put John Barker's visitors ahead on 28 minutes.
'Side could have equalised but Aaron Hunwicks missed a penalty on 34 minutes as Michael Walter's Sky Blues went into the break 1-0 down.
Despite their best efforts 'Side couldn't find an equaliser and St Margaretbury sealed the points on 72 minutes when Phil Lowen scored.
The result leaves 'Side in 17th in the league table. The sides will meet again on Tuesday at St Margaretsbury's Recreation Ground in the Second Round of the Gordon Brasted Memorial Trophy. Kick-off for that match is at 7:45pm.
'Side: Ryan Karrer, Garjay Thompson, Aaron Hunwicks (Bobby Sears), Harry Matthews, Euan Taylor-Reid, Ashley Pibworth, Manny Brown (Jacob Dingli), Morris Gelashvili, Thomas Ngegba (Terry Anim), Dan Jones, Mattheus Santos
Subs Not Used: Jedidiah Brown, Adebola Sotoyinbo