Harbaugh repeatedly stated in his postgame news conference that he was "bitterly disappointed" in the crew, led by referee Daniel Capron.
The most critical call to the outcome came on a J.T. Barrett rush on fourth-and-1 from the Michigan 16-yard line with Michigan leading 27-24. Officials signaled first down and upheld the play after replay review. Ohio State's Curtis Samuel raced into the end zone on the next play, ending the game.
"It wasn't a first down, by that much," Harbaugh said, holding his hands about a foot apart. "I'm bitterly disappointed in the officiating today. That spot, the graphic displays, the [pass] interference penalties, the one not called [for] us on Grant Perry, clearly was being hooked before the ball got there. And the previous penalty, they called on Delano Hill, the ball's uncatchable and by the receiver.
"So I'm bitterly disappointed in the officiating. Can't make that any more clear."
Michigan was flagged seven times for 59 yards, including an unsportsmanlike conduct penalty on Harbaugh late in the third quarter. Ohio State scored two plays later to cut its deficit to 17-14.
"They could have been watching the game [rather than being concerned] that you throw a hat, you throw your script toward your sideline," Harbaugh said. "That's a penalty? [The official said], 'Well, it is in basketball.' Well, this isn't basketball. He told me that he officiates basketball. It would have been a technical in basketball.
The Big Ten released a statement stating the "the conference has a process and procedures that it follows in evaluating these situations, and will not have any further comment at this time."
Former Nebraska coach Bo Pelini was fined $10,000 for making profane remarks about officiating after a 2013 game against Iowa.
Harbaugh said the non-call against Ohio State cornerback Gareon Conley, defending Michigan's Perry on third-and-4 in the second overtime, "really benefited them, getting that gift." The second-year coach added that he's been in other big games where the officiating played a huge role but "not to this level."
"There were some outrageous calls," he said, "including the one that ended the game. It had a good camera angle on it. The ball doesn't make it to the line. Gave them a first down."
Michigan players also felt Barrett was short on the fourth-down run.
Linebacker Mike McCray said Michigan had to move on to the next play and still had a chance to stop Ohio State.
"We didn't get the call that we wanted," McCray said. "Coach Harbaugh has his opinions and we back him up on what he has to say, just like he backs us up."