"This is a sour taste," the 7-footer said after Wisconsin's 74-73 loss to Kentucky in a thriller in the Final Four. "We are going to be back next year. We are going to be better than ever. We will all be ready."
The keyword is "all," because it sounds like Kaminsky and forward Sam Dekker are coming back in the fall. If that's the case, Wisconsin figures to lose just senior guard Ben Brust from its top-eight rotation - giving coach Bo Ryan a good shot to make another deep run into March.
First, though some well-earned rest for these energetic but weary Badgers (30-8).
Their year began before the college football season even kicked off with a five-game exhibition tour in August through Canada, a trip designed in part for Ryan figure out what he had on a squad that lost its starting frontcourt from the previous season. At the time, Kaminsky was an unknown quantity, while Dekker was making the leap from top bench player to starter.
Throw in the three-man starting backcourt of Brust, Traevon Jackson and Josh Gasser, and things worked out just fine.
The Badgers got off to a program-best 16-0 start and climbed to as high a No. 3 in the AP Top 25. They endured a 1-5 midseason slump before going on an eight-game tear headed into the final week of the regular season.
Finally, they had a thrilling four-game winning streak through to the NCAAs before falling short to Kentucky. It was the first trip to the Final Four in Ryan's 13 years in Madison, and the program's first Final Four appearance since 2000. Wisconsin was a victory short of tying the school's season record in 2007-08.
They had blowouts, comebacks and nail-biters. Athletic teams repeatedly tried to exploit Wisconsin in the lane. For the most part, they withstood the pounding until the very end against the Wildcats.
"No matter what the situation, we're always going to make a challenge or make a comeback ... to get yourself in a position to win," Brust said Saturday night.
Wisconsin will miss Brust's veteran savvy and 3 point-prowess.
Still, the Badgers should be just as good - or even better next season.
Kaminsky (13.9 points) and Dekker (12.4) will benefit from another year of experience, while Jackson (10.7) is Ryan's trusted floor general.
Josh Gasser (8.8) played well in returning from a knee injury that knocked him out in 2012-13. The team's top defensive player, Gasser could be relied upon to knock down more 3s after hitting a team-high 43 percent from behind the arc.
Ryan went with the same starting five the entire 38-game season, appropriate for a program known for its discipline and consistency.
But the contributions stretched to the bench. Freshman Nigel Hayes (7.7) carried the team through stretches in Big Ten games.
Another freshman, Bronson Koenig, displayed some flash as Jackson's backup at the point. He should capably join the three-guard rotation in place of Brust. Junior Duje Dukan provided valuable minutes of rest up front for Kaminsky and Dekker.
Freshman Vitto Brown seems poised for more minutes up front, while Wisconsin will add 6-foot-8 Ethan Happ from the 2014 recruiting class.
Ryan will have a couple more bodies up front, plus a few young guards coming off redshirt seasons. But there's still a ways to go before he can determine whether next season's squad can better limit opponents in the paint.
There is such a high standard for defense in Madison. This year's team held foes to 63.7 points per game coming into the Final Four - good for 37th in the country. Still it was the first time the Badgers finished out of the top 10 since 2005-06.
"When you look through the game, we know that we could have been better," Hayes said. "We know what it takes to get back here, and hopefully now we can repeat it."
(Copyright 2014 The Associated Press. All rights reserved. This material may not be published, broadcast, rewritten or redistributed.)