Bury paid the penalty for failing to capitalise on their first-half dominance at the Lancashire FA headquarters in Leyland.
They conceded the opening goal after the interval and they went further behind when keeper Holden made a fine save with his leg before the ball was hammered into the roof of the net from the edge of the six-yard box.
Bury threw caution to the wind and within a minute substitute Kieran Maplesden headed Bury a lifeline from the edge of the box with his first touch.
The cup final defeat followed Bury's 2-0 victory at bogey team Bolton Lads Club in the LAL Premier Division.
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