In a blistering start, the home side scored four within 12 minutes, with strikes from Victor Adeboyejo, Joe Powell and Gassan Ahadme's double taking the game away from the Foxes youngsters.
Tawanda Maswanhise and Ethan Fitzhugh pulled two back for the visitors before the break, but no further goals in the second half led to defeat for the visitors against senior opposition.
Fresh from defeating Blackburn Rovers Under-21s 4-0 on Saturday afternoon, Leicester took on the Sky Bet League 1 outfit in their first group stage match, making one change as Fitzhugh came into the starting XI, replacing Oliver Ewing.
Following a tricky start to the league season in tier three, with one point from their opening six games, the Brewers were looking for a confidence boost and found themselves ahead inside four minutes as Ahadme fired past Chituru Odunze.
It was almost two when Powell's volley did not quite dip enough to test City's shot-stopper, landing on the roof of the net, but three minutes after the opener, Albion did grab a second. Tom Hamer crossed for Ahadme to head home and notch his brace.
Terry Taylor's free-kick soon led to the third, eventually headed in by Adeboyejo in the ninth minute. And on 12 minutes, it was four. Ahadme picked out Powell to finish past Odunze.
The Foxes started to threaten for the first time when Kasey McAteer thought he was through, but the offside flag went up after he sent the ball past Viljami Sinisalo and also wide of the far post.
Back at the other end, Powell tried to whip a free-kick around the wall, but was unable to get enough bend on the ball to send it into the far corner.
City showed character to keep at it and could have pulled one back when in-form forward Maswanhise cut onto his left and hit the upright, before his second effort on the rebound was palmed away by Viljami Sinisalo. Wanya Marcal-Madivadua's shot on the follow up was then blocked by Cameron Borthwick-Jackson.
Powell soon got the better of Shane Flynn and crossed for Ahadme, on a hat-trick, but the striker blazed over the bar, and that proved to be a turning point.
Sammy Braybrooke's driving run through the middle led to a chance for Maswanhise, who made no mistake in curling the ball into the far corner.
It was game on 60 seconds later, as Flynn's low cross from the left eventually found its way through to Fitzhugh, who composed himself before sending the ball beyond the 'keeper.
Leicester switched system and personnel early in the second period, with Iestyn Hughes introduced in place of Will Alves. Fitzhugh soon had a golden opportunity to further reduce the deficit but could only fire straight at Sinisalo, who parried his powerful strike away from danger.
Pressure started to build from Flynn's shot, which was blocked, falling to Joe Wormleighton, whose cross was flicked towards goal by McAteer, but subsequently saved.
Burton's first real attempt of the second period came 20 minutes after the break as captain John Brayford tried his luck from range, narrowly missing the outside of the post.
City, though, were enjoying much more possession as the game wore on, with Burton content to sit further back.
They still had opportunities and substitute Charlie Lakin could not take his to further enhance the scoreline with 10 minutes to play, slicing his shot wide after the ball fell to him on the edge of the area.
Burton substitute Quevin Castro was given a second yellow card after 90 minutes but there was little time for Leicester to capitalise on their man advantage.
Major moment – Early goals blew City away
The result was decided in the first 12 minutes with the Brewers ruthless in their attacking game, scoring four. Despite a spirited fightback, including two goals, there was no way back for City's youngsters.
Where do we stand? – Third in the group
City sit third in Northern Group H after matchday one, with Burton leading the way on three points, while Bradford City are second after beating Sheffield Wednesday, who occupy fourth spot, 3-1.
Coming up – Brighton at home
Brighton & Hove Albion Under-21s visit LCFC Training Ground on Saturday (1pm kick-off) as the Foxes return to Premier League 2 Division 1 action.
In the Papa John's Trophy, meanwhile, City's next group stage fixture is away to League 2 outfit Bradford on Tuesday 4 October (7:30pm kick-off).
The details...
City: Odunze; Wormleighton; Appiah, Brunt (c), Flynn (T. Pennant 75'); Braybrooke, McAteer; Marcal-Madivadua (K. Pennant 66'), Alves (Hughes 52'), Fitzhugh (Popov 66'); Maswanhise.
Subs not used: Doherty, Wilson-Brown, Cover.
Goals: Maswanhise 38', Fitzhugh 39'.
All times BST.