Steve Cotterill's men headed to League One high-flyers Wigan in the knowledge a win or draw would see them through to the knockout stages.
But a changed Town side, featuring six regular starters, were undone by a goal in either half from an extremely youthful Latics outfit, for whom goals by academy pair Adam Long and Chris Sze saw them leapfrog Shrewsbury into second and into round two.
The reverse means Shrews have just a single clean sheet from 22 games this season. Cotterill would've been happy to qualify for the knockout stages, which begin at the start of next month - and made changes at the break to try to inspire his side - but it was to be a seventh away defeat from 10 this season.
Cotterill had said he planned to use a stronger side than in the two previous group games and the headline inclusion was Josh Vela, making his return from a knee injury after more than six weeks out.
Vela played 90 minutes and looked to have come through unscathed in Town's big plus on the night.
He was joined in the visitors' XI by young full-back Callum Wilson, the former AFC Telford academy defender who made his senior debut in the last tie.
Sam Cosgrove and Tom Bloxham were paired in attack, initially in a 4-4-2 before Cotterill switched system after a bright Wigan start.
Leicester loanee Khanya Leshabela was also in for just his fourth Town start, while Shaun Whalley was well enough for the bench following a calf issue. There was no place for Daniel Udoh, who still travelled to Wigan.
The Wigan side consisted of six academy players as Leam Richardson shuffled his options on a must-win evening.
A lively opening to the tie befitted a stadium much fuller than the attendance inside the DW.
Ex-Latics youngster Cosgrove tested home skipper Jamie Jones in goal with an arrowed strike from 25 yard that drew a diving save inside 30 seconds.
The youthful hosts struck back immediately, after Town youngster Wilson collected an early caution. Former Peterborough and Ipswich trickster Gwion Edwards shot just wide from distance.
The returning Vela almost marked the occasion moments later. Luke Leahy broke well down the left and his low cross was helped on by Cosgrove to the midfielder, whose angled low strike was blocked.
Vela was sharp in the opening exchanges and showed no sign of rust.
But Town fell behind after nine minutes. A set-piece was not completely cleared and Tom Pearce's delivery from the left was met by the unchecked defender Long, who powered his header high beyond the helpless Harry Burgoyne.
A shutout continues to prove elusive for Cotterill's men, who like at Stratford fell behind early on. And the boss changed from 4-4-2 to 4-5-1, switching Vela into the middle and Bloxham to the right, after 15 minutes.
A pause in play followed as young Latics right-back James Carragher, son of Jamie who was watching in the stands, was stretchered off with what looked a serious injury following a 50-50 challenge.
Cotterill shuffled his system again and eventually settled on the familiar back three, which his side appeared comfortable in. Bloxham almost worked an opening after half hour following a slip by defender Long, who recovered well.
The final 10 minutes of the first period were played in the middle third but Town forged a chance from a set-piece right on 45 minutes as Aaron Pierre headed Leahy's free-kick delivery over.
Burgoyne made a flying fingertip save to tip Edwards' curling strike over in stoppage time.
Cotterill turned to George Nurse and Whalley at the interval, with his charges needing to turn it around to qualify. Nathanael Ogbeta and Pierre were withdrawn.
Whalley, playing alongside Cosgrove and Bloxham, made an instant impact. He darted on to a ball over the top and smartly flicked the ball over a defender's head before prodding a half-volley goalwards, but Jones made a smart save.
Nurse headed Leahy's resulting corner wide of the left post.
Wigan punished their visitors barely a minute later. From very little danger, Nurse was beaten to a bouncing ball by the sprightly Sze and the 17-year-old found himself through on goal.
The teenager showed ice-cool composure to dink a finish over Burgoyne to give Salop a mountain to climb eight minutes after the restart.
Early second-half promise wore away as Town showed little sign the two goals required to qualify would arrive and Cotterill's men duly bowed out.
Wigan Athletic (4-2-3-1):
Jones (c); Carragher (Baningime, 21), Long, Robinson, Pearce; Smith, Adeeko (Costello, 77); Edwards, Aasgaard, Massey; Sze (McHugh, 77).
Subs not used: Tickle, Power, Lang, Hughes.
Shrewsbury Town (4-4-2):
Burgoyne; Wilson, Ebanks-Landell (c), Pierre (Whalley, 45), Ogbeta (Nurse, 45); Vela, Leshabela, Davis, Leahy; Cosgrove (Caton, 74), Bloxham.
Subs not used: Bevan, Bennett, Pyke, Bowman.
Attendance: 1,121 (37 Shrewsbury fans)
Referee: Scott Oldham