Georgetown and Jabril Trawick will take on a familiar foe n the NIT. (John Minchillo/AP)

Georgetown Coach John Thompson III tested his Hoyas mightily this season, scheduling a slate of rigorous nonconference opponents that included Kansas, Michigan State and Oregon.

But that pluck — along with victories over the Spartans, Virginia Commonwealth and Creighton — failed to convince the NCAA tournament selection committee that the sputtering Hoyas warranted a spot in the 68-team field Sunday.

As a result, Georgetown (17-14, 8-10 Big East) will miss the NCAA tournament for the third time in Thompson’s 10 years on the Hilltop and the first since 2009. The Hoyas’ consolation prize is a No. 4 seed in the National Invitation Tournament and an opening-round matchup with former Big East foe West Virginia (17-15, 9-9) on Tuesday.

It’s an old-school matchup (Georgetown holds a 26-25 edge in its series with West Virginia) in an old-school setting.

As the higher seed, the Hoyas will host Tuesday’s game, which is scheduled to tip off at 7 p.m. But because Verizon Center has a previous scheduling commitment, the Georgetown-West Virginia clash will be staged at 2,500-seat McDonough Arena on campus.

“I wish it was not an old foe, just because there is very much a familiarity with how we do things and how they do things, but we’re excited,” Thompson said in a telephone interview Sunday night. “There are many teams whose season is over right now. Are we where we want to be? No. But are we still playing and looking for a championship? Yes.”

Tuesday’s victor will advance to play either top-seeded Florida State or Florida Gulf Coast, which kicked off its Cinderella waltz through last year’s NCAA tournament by toppling second-seeded Georgetown in the opening game.

Thompson and West Virginia’s Bob Huggins matched coaching wits for five seasons as rivals in the former Big East.

The Mountaineers bolted for the Big 12 in 2012. And this season, what remained of the Big East splintered into two conferences, with most of its big-time football-playing members rebranding themselves as the American Athletic Conference and Georgetown and its basketball-driven brethren forming a reconstituted Big East that added Creighton, Butler and Xavier.

Georgetown was expected to be a force in the new Big East this season. The Hoyas had reached the NCAA tournament in four consecutive years. Last season, paced by Big East Player of the Year Otto Porter Jr., they tied for the league’s regular season title and earned a No. 2 seed in the NCAA tournament.

But their 2013-14 campaign was marred by misfortune and ended in disappointment. The Hoyas lost five of their last seven games, finished with a losing conference record for just the second time in Thompson’s tenure and let a chance for an at-large NCAA tournament bid slip through their grasp by losing to the Big East’s weakest link, DePaul, in their opening game of the conference tournament.

It was Georgetown’s first loss to DePaul since January 1994.

Though the Hoyas’ lost their season opener to No. 19 Oregon, their long-term prospects looked bright with UCLA transfer Joshua Smith, a 6-foot-10, 350-pound center, exploding for 25 points in his debut.

But the rebuilding plan in the post-Porter era soon hit a snag with news that versatile forward Greg Whittington, who was recovering from surgery on a torn ACL, had been dismissed from the team.

In January, just shy of the season’s mid-point, Thompson announced that Smith had been ruled academically ineligible for the rest of the semester.

That coincided with an injury to Jabril Trawick, the Hoyas’ best defensive player, who was sidelined five games with a broken jaw.

“We’ve had a lot of road blocks thrown our way,” Thompson said Sunday. “This year has not played out as we anticipated. That being said, the NIT is a great opportunity for us. Do we wish we were playing for the national championships in the NCAA tournament? Absolutely. But the NIT, particularly in the last two years, has changed. It’s something that we would be very proud and we really are going to go out and try to win.”