"It needs to be somebody who is going to excite us, excite our support," Winkelman told the club's official website.
"Like our city, we have big ambition - this stadium was built for top-flight football and that's where we want to get in the future.
"We believe in what we're doing and we believe in the future of the football club and the city, but I want to start achieving something on the pitch - it's about the trophies that you win, the memories you create and I want to start doing that more."
Winkelman added: "Our supporters have been through a lot. It's always been a difficult journey. I hope they know that our commitment is greater than ever.
"I'm the biggest supporter of this football club - I know what I want to see and I think I'm in good company with the rest of our supporter base."
Robinson, 36, who had been the third-longest serving manager in the top four divisions, led the Dons to the Championship in 2015 but was unable to keep them there beyond one season.
The Dons have yet to win at home in the league this season and are outside the relegation zone only on goal difference after taking one point from their last five matches.