The Latics came flying out of the blocks and led 2-0 after 25 minutes through Roger Espinoza and Jordi Gomez. But the Dons shocked the DW Stadium by going in level at the break thanks to two strikes from Ben Reeves.
Patrick Bamford levelled with eight minutes left, and it was the League One side who were pushing for the winner in the closing stages.
"I never felt we were in control, not one little bit," acknowledged Rosler.
"But when you are leading 2-0 just before half-time, and 3-2 just before full-time - with the experience we have in the side - we should be managing the game better.
"I am disappointed that we weren't good enough in the decisive moments in the game.
"We had players who have played in the Premier League, and with the experience we have in the camp I expected us to see it out.
"We had a plan, which was working well, but having got to 2-0 up we stopped it - we did it half-hearted.
"I had told my players how good MK Dons could play, especially when you give them time and space on the ball, and they were cutting through us.
"That was not the plan, and it ended up costing us dearly."