Goals either side of half time from Carl Baker and Nicky Maynard sentenced the Owls to just their fifth Championship defeat of the campaign.
Gary Hooper stepped up off the bench to claim his first goal in Wednesday colours to reduce their arrears in the 77th minute but it proved too little too late.
Defeat means Wednesday fall to ninth in the table on goal difference, four points adrift of the play-off positions.
And Carvalhal said: “It is difficult for me to explain what happened in the first half.
“I was disappointed with our first half performance. It was a shadow of our team. We didn’t control the game and missed a lot of passes.
“When we pressed, we didn’t press as a collective. MK Dons deserved to be leading.
“It was very easy for them to play inside of our team so that is something we must correct.
“We talked with the players and we made a change at half-time. We put more players in attack.
“We have heart and soul in our team and we believed we could get back into the game.
“We tried hard at the end to get a draw and the positive part of our game was the way we reacted and finished the game on the up.”
Midfielder Alex Lopez was taken off after picking up an injury while Michael Turner played through the pain barried late. Along with Sam Hutchinson (hip), Lopez and Turner are doubts for Sunday’s Hillsborough clash with Wolves.