Farsley are all but relegated after slumping to defeat at York.
With one game left, Celtic are three points behind 20th-placed Halifax but with a vastly inferior goal difference.
Martyn Woolford put the hosts in front on 11 minutes when he converted Andy McWilliams' cross and Leo Fortune-West made it 2-0 from Woolford's corner.
Simeon Bambrook gave Celtic hope on 73 minutes when he headed in a corner but substitute Richard Brodie's quickfire double wrapped it up for York.
York: Evans, Purkiss, McGurk, Parslow, McWilliams, Rusk, Panther, Beadle, Woolford (Brodie 71), Fortune-West, Sodje (Shepherd 82).Subs Not Used: Robinson, Mimms, Boyes.
Booked: Purkiss, Sodje , Brodie.
Goals: Woolford 11, Fortune-West 20, Brodie 84, 90.
Farsley Celtic: Aspden, Scott McNiven, Iqbal, Krief, Downes, Knowles, Watson (Prendergast 46), Reeves, Torpey, Bambrook, David McNiven (Heath 67).Subs Not Used: Stamer, Tuck, Backhouse.
Booked: Scott McNiven, Bambrook.
Goals: Bambrook 75.
Att: 1,886
Ref: G Sutton (Lincolnshire).
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