The Shakers enjoyed the better chances but still slumped to their fourth straight home defeat after Andy Barcham snatched a 71st-minute winner for their League Two rivals.
That also condemned Bury to their second cup defeat in five days after losing 1-0 at Darlington in the Johnstone's Paint Trophy.
"It was not good enough and I can understand the frustration of the fans," said Knill.
"I'm frustrated, too, because to go out of two cups in a week is unacceptable.
"We look a little lightweight, some of the players need to stand up and be counted. We looked a soft touch."
BURY: Brown 6, Scott 7, Cresswell 7, Sodje 7, Buchanan 6, Bennett 6, Barry-Murphy 7, Dawson 6 (Baker 29, 6), Jones 6 (Racchi 82, 6), Bishop 6, Morrell 6 (Hurst 65, 6). Subs: Haslam, Futcher, Anane, Belford.
Tweet
