Richard Wilkins labelled the performance in the 3-0 FA Trophy defeat against Eastleigh as ‘naive’, but said their higher-league opponents were too good on the day.
The Blues’ run in the competition came to an end in front of 321 fans at Ram Meadow on Saturday in the first round.
Two first-half goals from Ben Strevens were followed by a second half header from Craig McAllister, both former Football League hitmen.
Tom Bullard and Billy Clark went closest for Bury, who could not find a way past the excellent Ross Flitney.
* Cup holders Bury Town play at Woodbridge Town in the Suffolk Premier Cup quarter final on Wednesday (7.45pm).