Holding on for 89 minutes, the Foxes were undone by a last-minute winner from Angeldahl on Wednesday, as the Citizens maintained their 100 per cent record in Group B by dispatching Leicester, who pick up their first loss of 2023.
There were four changes to the starting XI that beat Brighton & Hove Albion in the Barclays Women's Super League only three days prior, with academy players Ava Baker and Monique Robinson both included in the line-up, following their impressive displays in the back-to-back wins the week earlier.
Leicester started the game in a 4-4-1-1 formation, with captain Aileen Whelan playing in the hole between the two banks of four and Hannah Cain playing up top on her own, who was starting her third successive game since returning from injury.
Less than 10 minutes in, the ball was in the back of the net when Baker got behind the Manchester backline and finished well past Sandy MacIver, however a glance at the linesman displayed a raised flag, and the scores remained level.
Over the next half an hour, there were little chances to report on, but it was the hosts who were looking most likely to create an opening, and they did just before the interval through a dangerous cross from Jemma Purfield.
Seconds before the break, the left-back whipped a dangerous ball into the box, into the path of Whelan who managed to get in front of the defender to guide her effort towards goal, but MacIver managed to pull off a spectacular save and turn the ball away from danger.
Immediately after the break, the Foxes were at it again when Baker tried her luck from range, cutting onto her right foot and striking from distance - but as the crowd lifted off their seats, the ball curled agonisingly the wrong side of the post.
Just before the hour mark, the visitors had their best chance of the game so far when Vicky Losada took aim from just inside the box, but thankfully for the Foxes' backline, the Citizen fired over, as the game still looked for its first goal.
Leicester arrived in Burton with only three substitutes, but they were keen to make an impact as Mackenzie Smith, who was introduced in the 71st minute, saw a chance fall her way with practically her first touch of the game.
As Baker paved the way, the young winger played the ball into the No.34 who hit a first time effort, but failed to test the Manchester 'keeper as the ball went wide.
Within the last five minutes, Man City looked to step it up a gear as they introduced Chloe Kelly and Laura Coombs into the game. Coombs came close to finding an opening in the 85th minute when she was given half a yard within close proximity to Kirstie Levell's goal, but the 'keeper was able to make the stop and keep her side in it.
Academy player Jess Reavill came on to make her senior debut in the closing stages, but Leicester's hard work was to be undone in injury time, when Angeldahl was picked out in the box, and turned in a low effort, confirming the Foxes' fate.
Major moment - Injury time winner
With little to separate the two sides, it took until injury-time for either team to find a winner. Unfortunately for Willie Kirk's side, it came for the visitors when Angeldahl netted in the dying moments.
Who impressed? - Leicester's youngsters
Facing a title-contending side, with less than ample choices on the bench, was no easy task, but the young Foxes of Ava Baker and Monique Robinson carried on their impressive form and put in another solid shift, showing the manager their ability to play in the first team.
Where do we stand - Third in Group B
The loss sees Leicester finish in a respectful place of third in Group B in the League Cup, on six points from four fixtures, but sadly it was not enough for the Foxes to progress in the competition.
Coming up - Tottenham Hotspur (A)
Following the midweek match-up with Man City, Leicester return to league action as they face Tottenham Hotspur on Sunday 22 January (2pm GMT kick-off) at Brisbane Road.
The details…
City: Levell; Simon, Howard (Reavill 89'), Plumptre, Purfield; Baker, Tierney, Robinson, Pike; Whelan; Cain (Smith 71').
Sub not used: Lambourne.
All times GMT.