Afterwards, Johnson says that he and his teammates were confident throughout the game, despite being down going into the half.
"It was a tough game from the start," Johnson said. "We didn't feel going into half that we were down nine. We felt good about ourselves and we had a few easy shots that we didn't finish, a few defensive rebounds that we let them get, so we felt good going into half.
"We just tried to stay with it and grind it out. When you are at Michigan with a hostile crowd and great team that they are, it's going to be tough all the way through."
Arizona's mental state allowed it to stay in the game due in large part to the confidence that its head coach put in his players.
"Coach was telling us at half we're good," Johnson said. "We went into half with six turnovers, so that was an area where we wanted to improve at. We just stayed loose, stayed free, and people made shots in the second half.
"That's what we work out for, that's what we're in Tucson all summer for, is that grind it out mentality. Keep on pushing, keep on pushing, and finally at the end they broke."
Nik Stauskas finished with 14 points for the Wolverines, but it was on 4-11 shooting and he was never able to get comfortable.
"I felt that he got a few easy ones," Johnson said. "He got the baseline drive, but other than that I felt I did pretty good on him. That was my main job coming into this game, was to limit his touches. He's such a great player, he is going to bounce back. Everybody is going to have games like those, but I am definitely happy with what I did."
Michigan is going to be one of the most hostile environments the Wildcats will see all season, but the early schedule allowed them to avoid being intimidated.
"I think the San Diego State game, Duke, and Drexel game were really big for our young guys to get their feet wet a little bit in road environment and it worked out," Johnson said.