The Owls failed to win for the fifth game in a row in all competitions.
The Owls fell behind after 25 minutes, and while Carvalhal's post-match comments suggest that he probably would have strongly criticised his team at the break, the Dons' lead was doubled five minutes after half-time through Nicky Maynard.
And Carvalhal was in no doubt as to why his side had fallen to the defeat (via Star).
"It is difficult for me to explain what happened in the first half," he said.
"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."
Although the Owls went into the game without a win in their last four in all competitions, their results suggested that there was much reason for optimism going forward.
Their only defeat in the recent run was against Premier League club Stoke City in the Capital One Cup, while they also secured away draws against rivals for a play-off spot, Blackburn Rovers and Cardiff City, and a home draw against automatic promotion chasing Derby County.
However, Karl Robinson's side were in the Championship's bottom three before last night's game, and thus it was a game that Wednesday would have known that they needed to win to help avoid falling right back into the huge pack of sides chasing a top six spot.