The 2-0 loss to Celtic B was their second successive ‘Old Firm’ defeat after going down 1-0 away to Rangers B the previous week.
Celtic scored both their goals in the first half, with Moffat giving them the lead after 20 minutes before striker Carse doubled their advantage after 33 minutes.
On Tuesday Berwick were home to Edinburgh University when they recorded a 3-0 win.
They took the lead on the stroke of half time with Jamie Pyper netting after 45 minutes and in the second half they secured the victory with further goals from Lewis Baker after 51 minutes and Lewis Allan after 73 minutes.
The win puts Berwick ninth in the table on 28 points and on Saturday (November 13) they are away to Civil Service Strollers.