"We pretty much did everything we could to get this win," Johnson said. "I am proud of our team's performance and how everybody fought and stayed with it, but I am just disappointed.
"All of the work you put in your whole life basically for this moment and we came up a little short, but we had a great season, great performance, and way to fight."
Johnson was called for an offensive foul late in the game, but he did not want to focus too much on the controversial call.
"It probably could have gone both ways," he said. "It was a great play by their defender. Obviously I wish it would have gone the other way, but it happens."
Arizona got one more opportunity at the end of the game, but failed to get a shot off.
"It was a great play by Rondae to tip the ball off him," Johnson said. "We had that second chance, it was definitely a better feeling than them having the ball.
"It was a little iso for me to left. If I had to go back and do it again I would probably take one less dribble so I can get the shot off, but that is how it was drawn up."
One of the key factors in the game was that the Badgers did not let Arizona get out in transition where it has been so successful this tournament.
"They had a great game plan," Johnson said. "They knew that we like to do that and saw previous games. Their coach is one of the best coaches in the country, so we were expecting a great game plan."
When asked what the future holds for Johnson and his teammates, attention remained on Saturday's disappointing result.
"We're not thinking about that right now," Johnson said. "This is basically our whole lives working for this moment. Our team came together this summer with one goal in mind- to work hard and progress so we could get to this point and get past it."