MK Dons' Will Grigg and substitute Benik Afobe scored two goals apiece as United's defensive frailties were ruthlessly exposed by their enthusiastic lower division opponents who took advantage of playing against a second-string side.
Grigg capitalised on United's mistakes to score either side of halftime before Afobe compounded the visitors' misery with two late goals, the first seconds after coming off the bench.
Dutchman Van Gaal is still without a competitive victory since taking over at United in the close season and he will be desperate for British record signing Angel Di Maria to play after he signed from Real Madrid earlier on Tuesday.
"It's a matter of making errors at wrong moments," Van Gaal told Sky Sports. "When you see the goals against us, I believe they were big errors that you cannot make.
"Then it was 2-0 and it was very difficult to come back into the game. In the second half we created a lot of chances and didn't have the luck to score. Then two more errors and it's 3-0 and 4-0."
It was United's first outing in the second round of the competition since 1995 and the first time they had conceded four goals in a League Cup match against lower league opposition.
Van Gaal left out several first-team regulars including captain Wayne Rooney and strike partner Robin van Persie but asked if he regretted making so many changes, he said: "No, you have to analyse the problem and I've done that.
"We have nine injuries and a very young team. I've seen them trying to do their utmost best so you cannot expect more."
West Ham United lost 5-4 on penalties at home to Sheffield United following a 1-1 draw after extra time, while fellow top-flight sides Leicester City and Burnley went down 1-0 to visiting Shrewsbury Town and Sheffield Wednesday respectively.
Dwight Gayle scored a first-half hat-trick as Premier League crisis club Crystal Palace, without a manager after Tony Pulis left the club, enjoyed a 3-0 win at third-tier Walsall.
Newcastle United won 1-0 at Gillingham, Southampton beat Millwall 2-0 away, Swansea triumphed 1-0 at home to Rotherham United and West Bromwich Albion beat visitors Oxford United 7-6 on penalties with the teams locked at 1-1 after extra time.
Following Manchester United's 2-1 Premier League defeat by Swansea City, their first opening day loss at home since 1972, and a toothless 1-1 draw at Sunderland, they should have welcomed a seemingly straightforward game at lowly opponents.
After a bright start, though, they found themselves behind.
Jonny Evans gifted the hosts possession in his own penalty area and Grigg punished him with a cool finish after 25 minutes.
Just after the hour mark the hosts doubled their lead and again United were the masters of their own downfall.
Another misplaced pass was capitalised on by Ben Reeves whose cross was steered home by Grigg's audacious chested finish.
Afobe was brought into the action after 68 minutes and immediately scored with a low shot which flew past United goalkeeper David de Gea.
Afobe added a fourth after 84 minutes, bundling his way past several defenders before firing into the corner to complete a famous win for a team who were only founded in July 2004.
"I'm a little bit in shock... it's ridiculous and something dreams are made of," said MK Dons manager Karl Robinson. "My players and my football club, and the city in general, deserve credit tonight."