BURY can concentrate on fighting for League One survival after bowing out of the Checkatrade Trophy on Tuesday night.
Visitors Fleetwood eased in front in the third-round tie as Jordy Hiwula's 14th-minute opener was followed up by a 17th-minute penalty from Bobby Grant.
Substitute Harry Bunn roused a meagre home crowd as he pulled a goal back in first-half stoppage time, only for Hiwula to strike again on 50 minutes.
The Shakers hit back five minutes later through a first senior goal by half-time substitute Tsun Dai.
And despite finishing strongly, Bury could not avoid a seventh straight defeat as league rivals Fleetwood secured their place in the last eight.
Manager Chris Lucketti made eight changes to the side which lost 3-0 at Plymouth on Saturday, with new loan signings Connor Ripley and James Hanson, along with Greg Leigh, the only men to remain in the starting XI.
The Bury boss began with a 3-4-1-2 formation, with left-back Joe Skarz making his first appearance since the group win at Blackburn on October 3, while Leigh was at left wing-back and youngster Ryan Cooney was on the right.
The new-look line-up made a positive start with visiting keeper Alex Cairns having to tip Chris Maguire's 25-yard free kick against the post before Callum Reilly dragged a shot wide.
But a Fleetwood side that was entirely different to that which started Saturday's FA Cup draw with Leicester then charged into a 2-0 lead.
Conor McAleny shrugged off Eoghan O'Connell to latch onto Hiwula's through-ball and although his shot was well saved by Ripley, the rebound looped up for Hiwula to head into an empty net.
And the Shakers' defence was soon caught flat-footed again as Hiwula charged into the box before being tripped by Phil Edwards, with Grant firing the spot-kick into the bottom corner.
Fleetwood remained on top with McAleny dragging a shot wide before firing straight at Ripley, and O'Connell's miserable evening got worse as he was stretchered off to be replaced by Bunn, who played wide right as Lucketti rejigged his line-up.
Bunn's introduction boosted Bury as Maguire laid off for Reilly, whose shot from the edge of the box thumped against the Fleetwood bar.
Bunn then drifted in from the right and shifted the ball onto his left foot, curling inside the far post to score Bury's first goal in seven games – since their second-round win at Walsall on December 2.
Although some home fans had rightly been critical during the opening period, they rallied behind the players as they went back down the tunnel.
But shortly after the interval Edwards misjudged a long ball, allowing Hiwula to slot past Ripley.
Dai made his first appearance under Lucketti and then gave the Shakers hope, firing home from close range after Cairns turned a cross into his path.
And the Hong Kong youth international almost equalised moments later as his 20-yard strike was parried by Cairns, who blocked Ajose's follow-up.
Bury failed to maintain that momentum, with McAleny off target following a short corner, but Reilly and Ajose tested Cairns late on.
The visiting keeper then clawed away Maguire's long-range strike to deny the Shakers a penalty shoot-out.
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