If the ignominy of entering the competition at this phase for the first time since 1995 was not bad enough, United - who have begun their start to life under Van Gaal with a home defeat at Swansea City followed by 1-1 draw versus Sunderland - fared even worse than 19 years ago on Tuesday.
Beaten 3-0 at home, and 4-3, on aggregate by York City then, United went one worse as doubles from Will Grigg and Benik Afobe earned MK Dons an incredible win.
There were no such issues for fellow Dutch Premier League newcomer Ronald Koeman as he grabbed his first win when goals from Jack Cork and Graziano Pelle overcame Millwall 2-0.
United were not the only Premier League side beaten by lower-league opposition, West Ham United, Leicester City and Burnley also succumbing.
New boy Enner Valencia missed the crucial penalty for West Ham in a 5-4 shootout win for Sheffield United that followed a 1-1 draw in normal time.
Leicester, meanwhile, were beaten by Shrewsbury Town, Andy Mangan's stunning free-kick the only goal.
At Turf Moor, Burnley went down by the same scoreline as Atdhe Nuhiu's late penalty saw Sheffield Wednesday progress.
Newcastle United, Crystal Palace and Swansea City did not endure the same fate.
Newcastle beat Gillingham 1-0 thanks to John Egan's own goal, Palace overcame Walsall 3-0 through Dwight Gayle's hat-trick and Bafetimbi Gomis' first Swansea goal helped the Welsh club to overcome Rotherham United.
Things went much more smoothly for Championship clubs, with Bournemouth beating Northampton Town 3-0, Fulham overcoming Brentford 1-0 and Bolton Wanderers triumphing 3-2 at Crewe Alexandra.
There were also wins for bitter rivals Derby County and Nottingham Forest, who beat Charlton Athletic and Huddersfield Town 1-0 and 2-0 respectively.
Middlesbrough and Norwich City had few problems brushing aside Preston North End and Crawley Town, each easing to 3-1 successes.
Cardiff City were made to work harder, edging a five-goal thriller at Port Vale 3-2, and Reading won 1-0 at Scunthorpe United.
In the night's other games, Brighton and Hove Albion triumphed 4-2 at Swindon Town and Doncaster Rovers beat Watford 2-1 away from home.