The club said pre-match that it was looking forward to a new cup campaign so will be disappointed to have fallen at such an early hurdle.
New manager Gordon Herd has had a week or so to work with the squad and will this week aim to guide them to a home victory over Broxburn Athletic.
The management team are moving quickly to mould their squad and have this week announced that experienced right back Scott Stevenson has been made available for transfer.
As well as cup ties, there was some league action for East of Scotland Football League clubs at the weekend.
Lothian Thistle Hutchison Vale made the journey to meet Camelon and returned from the central belt with all three Premier Division points thanks to a 3-1 win.
This weekend Camelon host Blackburn United.
Sauchie had better luck on Saturday, taking all three points from their league meeting against Hill of Beath thanks to a 4-2 win.
Sauchie make the journey to face Jeanfield Swifts this Saturday.
Tranent Juniors continue to lead the way in the Premier League and, at the weekend, beat Newtongrange Star 1-0.
This week Tranent face Musselburgh Athletic.
After enjoying a free week last weekend, Dunipace resume their Conference A campaign on Saturday.
The local side will be aiming to dish out some capital punishment when they travel to Edinburgh United. Kick off is 2.30pm.