Michigan was outgained 476-336 as Scarlet Knights quarterback Gary Nova threw for a career-high 404 yards and three touchdowns with no interceptions.
"We had the game won, bottom line," Mattison said of the offense's 24-point performance. "If you're a great defense, you do what you have to do in that game to stop them and you win. It may not be pretty, but you win. I agree with you, our offense did a good enough job to win that football game, and it was up to us to have stopped them at that time, and we didn't. That's on me."
The loss, which dropped Michigan's record to 2-4 (0-2 Big Ten), comes amid rampant speculation over head coach Brady Hoke's job status.
It also marked Rutgers' first conference win as a member of the Big Ten.
The Wolverines host Penn State (4-1) on Saturday.
- Chris Johnson