Liversedge bowed out of the FA Cup at the first hurdle last Saturday, going down 5-2 at home to Guisborough Town.
Guisborough led inside seven minutes through Connor Smith but Vaughan Redford equalised only for French Under-16 World Cup winner Thibault Charmey to restore Town’s lead on the stroke of half-time.
Steve Robson made it 3-1 after 48 minutes but a Joe Walton header gave Sedge hope.
Tom Bligh struck after 75 minutes and as Sedge chased the game, Charmey sealed victory with a fifth.
Liversedge suffered a 3-2 defeat at AFC Mansfield in their opening Northern Counties East League Premier Division game on Wednesday.
They were 2-0 down inside 25 minutes after goals from Ryan Williams and Oliver Fearon before Joe Walton pulled a goal back before half-time.
Rhys Davies qualised in the 52nd minute only for Gary Bradshaw to hit Mansfield’s winner after 69 minutes.
Sedge host Armthorpe Welfare in their first home game tomorrow (Saturday).