NCAA selection committee chairman Kyle Kallander said UVU (47-12) was one of the last teams considered. UVU wasn't alone in its disappointment. Texas and Maryland were also left out of the tournament.
UVU was a bubble team due to strength of schedule playing against teams such as Missouri, which unexpectedly won conference tournaments and that played a large role in keeping the first Wolverine team from earning its first at-large bid to a NCAA Tournament.
UVU athletes have competed in NCAA events, including wrestling, where Ben Kjar earned All-American honors two years ago. The school's basketball team earned its first-ever postseason spot when it competed in the College Insider Tournament.
Utah Valley, which won its third consecutive league title, plays in the Great West Conference, which doesn't have an automatic bid. Even as the Wolverines went unbeaten in their league, their RPI, or power ranking, fell.
"I felt pretty confident, we won 40 of 41," senior pitcher Josh Swenson said. "We did all we could. We had a blast this year."
Utah Valley defeated three Pac-12 teams, including then-No. 4 Arizona. The Wolverines led the NCAA in a handful of categories, including wins, runs per game and slugging.
"I've heard from a lot of people, to get that first at-large bid is the most difficult," Madsen said. "This is a pretty special year. We got a lot of attention. We controlled what we could control."
Florida (42-18) was selected as the top overall seed and will host one of 16 four-team, double-elimination regionals that begin Friday.
The other national seeds, in order, are: UCLA, Florida State, Baylor, Oregon, North Carolina, LSU and two-time defending College World Series champion South Carolina.
The Associated Press contributed to this report.