Mangan, a free-transfer signing from Forest Green Rovers during the summer, scored the only goal of the night at the King Power Stadium to send the League Two Shrews into the third round.
It was nothing more than Micky Mellon's side deserved as there was often little to determine which team was in the top flight and the other three leagues below.
With one point from their opening two matches on their return to the big time, if City boss Nigel Pearson had been looking at this game as a springboard to get his team's season rolling, then he was sorely mistaken.
In addition to the Foxes and Manchester United, who were shockingly thumped 4-0 by MK Dons, West Ham were another top flight side dumped out by third-tier opposition when they were edged out in a penalty shoot-out by Sheffield United.
New signing Diafra Sahko put the Hammers level in the first half before a Winston Reid own goal levelled the game in the second period and another summer recruit, Enner Valencia, was the only man to miss from 12 yards sending the Blades through.
Oxford took West Brom all the way to penalties before the Premier League side prevailed 7-6 to reach the third round.
Australian defender Jason Davidson scored the winning spot-kick after Oxford captain Jake Wright had seen his effort saved by Boaz Myhill.
Bafetimbi Gomis scored his first goal in English football as Swansea progressed to the third round courtesy of a 1-0 win over Rotherham.
Swansea - winners of the competition two seasons ago - could never relax against resilient Rotherham from the Championship, but Garry Monk's men were always in control after Gomis' clinical first-half strike.
The decisive moment came after 22 minutes when Nathan Dyer found Gomis on the edge of the penalty area and the 12-times capped France striker followed up his smart turn with a clinical finish low past Millers' goalkeeper Scott Loach.
The forward latched onto Chris David's defence-splitting through ball to slide a low shot into the far corner to settle a hard-fought west London derby.
Substitute Nuhiu rifled home to settle the second-round tie at a half-empty Turf Moor after Jason Shackell had upended Jeremy Helan.
The Clarets had been in the ascendancy at the time but the contest overall was fairly even and the Owls had gone close when Burnley's Kevin Long struck the frame of his own goal.
Burnley wanted a penalty themselves in injury time when Ashley Barnes went down but nothing was given.
Capital One Cup round two results
FT AFC Bournemouth 3 - 0 Northampton Town
FT Brentford 0 - 1 Fulham
FT Burnley 0 - 1 Sheffield Wednesday
AET Crewe Alexandra 2 - 3 Bolton Wanderers
FT Gillingham 0 - 1 Newcastle United
FT Huddersfield Town 0 - 2 Nottingham Forest
FT Leicester City 0 - 1 Shrewsbury Town
FT Middlesbrough 3 - 1 Preston North End
FT Millwall 0 - 2 Southampton
FT Norwich City 3 - 1 Crawley Town
FT Port Vale 2 - 3 Cardiff City
FT Swansea City 1 - 0 Rotherham United
AET Swindon Town 2 - 4 Brighton & Hove Albion
FT Walsall 0 - 3 Crystal Palace
FT Watford 1 - 2 Doncaster Rovers
AET West Ham United 1 - 1 Sheffield United (Sheff Utd win 5-4 on penalties)
FT Milton Keynes Dons 4 - 0 Manchester United
AET West Bromwich Albion 1 - 1 Oxford United (West Brom win 7-6 on penalties)
- Sports & Recreation
- Manchester United
- Forest Green Rovers
- Bafetimbi Gomis
- Micky Mellon