CHARLOTTESVILLE — Less than 24 hours after the Virginia football team absorbed its most lopsided loss of the season in the ACC championship game, the mood among Cavaliers players and coaches grew considerably more upbeat when they learned they would be playing in the Orange Bowl for the first time.

Orange Bowl officials made the announcement Sunday, a few hours after the unveiling of the four teams selected to participate in the College Football Playoff. One of those teams, No. 3 Clemson, trounced the Cavaliers, 62-17, on Saturday night at Bank of America Stadium in Charlotte, but soon after the final whistle, Orange Bowl representatives spoke with Virginia Coach Bronco Mendenhall outside the team’s locker room.

The No. 24 Cavaliers (9-4), who are making their first appearance in a New Year’s Six bowl game, will face No. 9 Florida (10-2) at 8 p.m. Dec. 30 at Hard Rock Stadium in Miami Gardens, Fla. This is the second straight year Virginia has drawn an SEC opponent in a bowl game; last season, the Cavaliers beat South Carolina, 28-0, in the Belk Bowl.

“At this point, we look forward to learning everything we possibly can from this game, playing one more and hopefully achieving a 10th win,” Mendenhall said Saturday night. “[That] would mean a lot for this program, and another bowl victory.”

The Orange Bowl bid represents another milestone in Virginia’s ascension since Mendenhall took over four years ago. This season, Virginia won its first ACC Coastal Division title to earn a berth in its first conference championship game. That matchup came a little more than a week after the Cavaliers beat Virginia Tech, 39-30, to snap a 15-game losing streak to its instate rival.

The Hokies (8-4) also learned their postseason destination Sunday: They are headed to Charlotte to face Kentucky (7-5) in the Belk Bowl at noon Dec. 31. The bowl will be the final game in the decorated career of longtime Virginia Tech defensive coordinator Bud Foster, who is retiring at the end of the season.

Justin Hamilton, an assistant on the Hokies’ staff responsible for safeties, will be Foster’s replacement, the school announced Sunday. Head coach Justin Fuente also announced that assistants Zohn Burden (running backs) and Brian Mitchell (defensive backs) will not be back.

For Virginia, having three weeks until the Orange Bowl represents a significant benefit, given myriad injuries that diminished its roster against Clemson, which won its record fifth consecutive ACC championship game and extended its winning streak to 28.

Shortly before kickoff, the Cavaliers announced wide receiver Joe Reed would be unavailable because of an undisclosed injury. Reed leads Virginia in touchdown catches (six) and receptions (70) and is among the most dangerous kick returners in the nation.

Linebacker Jordan Mack was in uniform but was unable to contribute for more than a few snaps because of a sore ankle that has bothered him for several weeks, Mendenhall said. The defense already was without cornerback Bryce Hall, a senior who suffered a left ankle injury Oct. 11 against Miami that ended up requiring surgery.

“This is just right on track with all of our goals,” said Virginia linebacker Charles Snowden III (St. Albans). “We came up a little bit short on winning the ACC, but winning a bowl game was one of the goals that we all had, coaches and teammates alike, so that’s kind of the next one up.”

Navy to the Liberty Bowl

Unlike Virginia, Navy’s bowl berth isn’t a first for the Midshipmen — but it has been a while since they have had their end-of-season game in Memphis, where they will play Kansas State in the Liberty Bowl at 3:45 p.m. Dec. 31.

Navy (9-2) made its only other appearance in the Liberty Bowl on Dec. 30, 1981, when it lost to Ohio State, 31-28. The Mids return this year for their 24th bowl appearance — and 15th in the past 17 years — behind a rejuvenated defense and a talented quarterback, senior Malcolm ­Perry, who is a Tennessee native.

Navy, which has won four of its past five bowl games, was No. 23 in the final CFP rankings.

The Liberty Bowl will be the first meeting between Navy and Kansas State (8-4). The Mids ­haven’t played a Big 12 team since they beat current SEC member Missouri in the 2009 Texas Bowl. The Wildcats handed No. 4 Oklahoma — which is headed to the Peach Bowl, a CFP semifinal, against No. 1 LSU — its only loss of the season, a 48-41 victory Oct. 26.