Buxton crashed out of the FA Trophy at the second qualifying round stage, going down by a single goal at Sheffield FC on Tuesday night.
The Bucks struggled to match the tempo of the previous weekend when they impressed in the 2-2 draw with Marine.
The first real opportunity of the evening came for the away side when Craig King’s effort was turned behind for a corner.
From the resulting set-piece Ash Palmer rose highest only to see his header drop wide of the goal.
From then on Sheffield stepped up the intensity and were almost given a golden chance to open the scoring when Tim Ryan’s loose ball was pounced on by a home striker, only for backpedalling Bucks’ defenders to turn the ball behind for a corner.
Soon after the hosts made it 1-0 when Zeph Thomas finished off a good move by James Gregory, as he rolled the ball beyond Andy Warrington.
Sheffield were looking impressive on the counter and stepped up their game in the second half.
Warrington had to be agile to keep out three goal-bound efforts, one of which was a terrific one-handed save to deny an almost certain second goal.
Mark Reed was introduced just after the hour mark by manager Martin McIntosh in a bid to get the Bucks back in the tie and the forward saw his looping header land on the roof of the net not long after taking the field.
The hosts were at this stage looking comfortable and they thought they had grabbed a game-clinching second only for the assistant to flag a tap-in offside.
Despite that lifeline, Buxton failed to muster an equaliser which means Sheffield will host Gresley in the final qualifying round.
Bucks: Warrington, Black, Green, Ryan, Palmer, Stevens, Istead, Harris, Thornhill, King, Morris.