An early goal at the start of each half, coming from Callum Paterson and Will Trueman, saw the home side pick up their first points in Northern Group H, but neither team could qualify for the next round.
Three changes from the Premier League 2 Division 1 game against Fulham eight days earlier saw Shane Flynn, Zach Booth and Jahmari Lindsay come into the side as Ben Petty named a youthful XI, while the hosts made 11 changes from the weekend's Sky Bet League 1 fixture.
Although heavily beaten by the Cottagers, Leicester had triumphed over Bradford City on penalties in their previous encounter in this competition, giving themselves a chance to progress at the expense of senior opposition.
But it was the worst possible start as Wednesday's first strike on target hit the back of the net. Flynn conceded a free-kick on the edge of the box and the experienced Paterson stepped up, arrowing the ball into the bottom corner, with the game just eight minutes old.
City responded well and Flynn, playing in an unfamiliar central midfield position, managed to fashion space for a curling right-footed effort that had Cameron Dawson scrambling, though the 'keeper managed to tip the ball over the crossbar.
Will Alves soon got on the ball to good effect, running at the defence and twisting and turning before his shot angled away from the goal and the post.
The visitors soon won possession back high up the pitch, creating a chance for lone forward Chris Popov, who attempted an audacious overhead kick that failed to test Dawson.
Tawanda Maswanhise, with two goals in as many matches in the competition, was a whisker away from an equaliser, flashing a left-footed shot agonisingly wide of the far post.
Foxes captain Chituru Odunze had to be alert at the other end to push Leojo Davidson's low shot away from goal, and he was called into action again to hold the midfielder's header, before Alex Mighten and Malik Wilks both couldn't hit the target from either side.
It took seven second-half minutes for the Owls to double their advantage. Trueman initially found himself free in the 18-yard box, but Odunze produced a sharp shot, before the ball was recycled out to Jaden Brown and his cross was steered home by the youngster.
Brown was in the mood for more, wriggling his way through a couple of challenges before firing wide, ahead of crossing for Paterson, who also missed the target from inside the box.
A double City change looked to have changed the momentum, with Kian Pennant and Brandon Cover into the action with half an hour to play and it almost paid off when Alves struck the crossbar from range.
An even better opportunity arrived when Henry Cartwright's long ball was chased down by Maswanhise, who was taken down by Wednesday captain Jack Hunt. The forward stepped up to take but found Dawson unbeatable once more, making a diving save to push the spot-kick away.
Another two substitutions allowed Terell Pennant and Harvey Godsmark-Ford to enter the field, but it was the Yorkshire side in the ascendency. Paterson was off target from range, while Glover fired over after Paul Appiah cleared the ball off the line, preventing Trueman adding his second.
It just wasn't to be Leicester's night, and when Dawson fumbled a cross, Maswanhise missed the target, with two defenders back on the line to block his route to goal.
Major moment – The penalty miss
Tawanda Maswanhise has been a goalscoring machine for City's Under-21s at the start of this season but his failure to convert from 12 yards, coupled with a later miss from close range, proved pivotal in preventing a second-half comeback.
Who impressed? – Under-18s step up
Although the result didn't go their way, several of the Club's Under-18s players made their mark, including Jahmari Lindsay, Tom Wilson-Brown and Henry Cartwright, as well as Ben Grist from the bench.
Where do we stand? – Fourth in the group
City's youngsters finish fourth in Northern Group H, on two points, one point behind Sheffield Wednesday, while Burton Albion and Bradford City progress to the next round.
Coming up – Arsenal (H)
Arsenal Under-21s travel to LCFC Training Ground on Monday 24 October as Premier League 2 Division 1 action returns for the young Foxes (7pm kick-off).
The details...
City: Odunze; Wormleighton (Cover 61'), Appiah, Wilson-Brown (Godsmark-Ford 71'), Lindsay; Cartwright, Flynn (Grist 78'); Alves, Booth (K. Pennant 61'), Maswanhise; Popov (T. Pennant 71').
Subs not used: Doherty, Briggs.
All times BST.