The League One club pulled off one of the biggest upsets in the competition’s history as two goals apiece from Will Grigg and Benik Afobe sent United crashing out.
But Van Gaal was brutally honest when asked if the cup capitulation had left him stunned.
"I am not shocked," he told Sky Sports.
"We made errors in building up situations in the first phase, and when you make errors like that you give the match away."
After a promising pre-season, the wheels appear to be coming off United's campaign already, having previously picked up just one point in the Premier League.
However, Van Gaal wants the fans to stick by his team and his philosophy, urging the Red Devils' following to judge him in time.
"They have to believe in our philosophy," he said.
"We are building up a team and you cannot make (it) in one month, not in one year.
"Of course it's very disappointing but I hope they shall maintain their confidence in the club and in our philosophy because that philosophy takes time."
The Dutchman was disappointed to see his side concede goals due to individual mistakes - Jonny Evans with a glaring howler for the opener - but he was quick to defend his decision to make 10 changes from the team that drew with Sunderland on Sunday.
"You have to analyse the problem and then you have to take your matches and I have done that and I think the changes were good," Van Gaal added.
"But it's also risky to change and to play one against one and therefore Milton Keynes could score. You don't have to forget that we have nine injuries and we have a very young team. I have seen them trying to do their utmost best.
"So more, you cannot expect of players. We were also unlucky because they scored out of our errors at once and then you are always behind."
The defeat came just hours after the Red Devils completed the signing of Angel di Maria for a British record fee but Van Gaal is not expecting the Argentinian to be an instant saviour.
"He shall contribute very much in our way of playing. He is also a creative player," Van Gaal said.
"I can change the system with Di Maria as he can also play the wing and play in midfield. He can contribute and that's very important but we don't have to expect that tomorrow, the world has changed.
"He has to adapt to the culture of England, to the culture of the Premier League and to the philosophy of Manchester United."
MK Dons boss Karl Robinson admitted he was as shocked as anybody after watching his League One team claim a stunning 4-0 win.
"I'm a little bit shocked to be walking off and seeing the scoreline," Robinson told Sky Sports.
"It's ridiculous, it's something that dreams are made of for these players. We work hard here and you've seen a youthful energy in the team."
The United team was largely changed and missing many of its stars but Robinson was eager for his players to get due credit.
"They've got the superstars in the side and they're the ones that are in the public eye on a daily basis, an hourly basis to an extent, we're not," he added.
"So it's always easy to pick negatives in people than push the positives on the other people. I think my players deserve an awful lot of credit tonight. The football club does and Milton Keynes does. This is a game for Milton Keynes as a city."