Micciche has suffered four straight league and cup defeats at the start of his reign, a run which has left the Dons six points adrift of safety.
They could have gone in front at Oldham, with Chuks Aneke forcing an early save from home goalkeeper Johny Placide.
Robbie Muirhead fired just wide, but the visitors struggled to create any openings for the rest of a scrappy contest.
Oldham won it through captain Anthony Gerrard, who planted in a 40th-minute header from Ben Pringle’s corner.
The Latics squandered chances to double their lead, but they deserved a vital win.
Micciche said: “There are a lot of points to play for and, mathematically, we can still climb a long way up the table.
“We need that first win to give us momentum, but we can get ourselves on a decent run and I believe in the players .
“We can’t feel sorry for ourselves. Myself and (assistant manager) Keith Millen will do everything we can to find a way of winning that next game.
“I can’t fault the players’ efforts. We looked solid tonight and the one positive from the last four games is that we don’t look like getting opened up defensively.
“We knew this would be a scrappy game. The pitch was practically unplayable and it was always likely to be settled by a setpiece.
“I’m so frustrated that we weren’t the team to score it. We had the better of the play in certain areas, but I know the situation and I know we need to improve quickly.”
Oldham’s victory moved them out of the bottom four and boss Richie Wellens said: “Our attitude was spot on.
“In the first 10 minutes were passing it for fun and everyone was thinking we were playing well, but the pitch is shocking and we had to play the conditions.
“MK Dons want to play expansive football as well, so they need a better pitch just like we do.
“I’m buzzing with the result, although I don’t like telling the players to do things that are only right because they suit the conditions.
“After beating Bradford and drawing at Blackburn this is another good result, so I’m really pleased with the players.
“We have put ourselves in a better position in the table, but the teams around us will go on runs and we just have to focus on ourselves.
“Every single player applied themselves and put everything into the game.
“The clean sheet is obviously pleasing and it should give the players a lot of confidence.”
Uwe Rosler was sacked by Fleetwood following a 3-0 reverse at Doncaster which condemned Town to a seventh straight defeat in all competitions.
Cambridge interim head coach Joe Dunne was pleased with how his side adapted to beat Grimsby 3-1.