Since the beginning of last month, when the Georgetown men’s basketball team began to dig itself out of a five-game losing streak, Hoyas Coach John Thompson III has spoken repeatedly about his team’s scant margin for error in order to secure an NCAA tournament berth. Winning, he said, was the only guarantee of removing all doubt whether Georgetown belongs in the field of 68.

But the Hoyas were unable to make good on that mandate down the stretch, losing four of six at the end of the regular season and finishing two games below .500 in the overhauled Big East. The closing swoon has left Georgetown no alternative but to complete an improbable foray through the conference tournament to be guaranteed a fifth straight NCAA appearance.

The journey begins Wednesday night for the seventh-seeded Hoyas (17-13, 8-10 Big East), who will face DePaul in a first-round game that’s scheduled to tip off at approximately 9:30 at Madison Square Garden. The Blue Demons are the No. 10 seed after finishing with the worst record in the conference, including a pair of losses to Georgetown.

“We’re going to New York to win. Let me just say that,” Thompson said Tuesday, shortly before boarding the team bus for the first leg of the trip. “We understand that if you win, there doesn’t have to be a conversation, but I think if you look at the body of work, hopefully we are very much in the conversation.”

Georgetown ranks 54th in the RPI, a statistical measure used by the NCAA tournament selection committee to rank teams, after playing the nation’s 11th-toughest schedule, according to analyst Jerry Palm of CBSSports.com.

The Hoyas last won the Big East tournament in 2006-07 as the No. 1 seed. Since then, they have advanced to the championship game twice and last season lost in overtime to Syracuse in the semifinals, 58-55, in the Orange’s final Big East tournament appearance before joining the ACC.

This season, Georgetown failed in multiple attempts to move into position for a top-six seed and earn a Big East tournament bye, meaning it would be playing four games in as many days if it advances to the final. Consecutive losses in the New York/North Jersey area over four days were especially damaging.

The first came during the Hoyas’ most recent visit to the Garden on Feb. 16, where they were no match for surging St. John’s, 82-60. Georgetown could have moved above .500 in the Big East for the first time since Jan. 15 but instead fell behind by 18 at halftime in absorbing a loss that matched its most lopsided this season.

Then came a trip to Newark on Feb. 20 and another drubbing, this time against Seton Hall, 82-67, that all but dashed any realistic hopes of a bye. The 164 points allowed were the most in consecutive games this season for Georgetown, which for the most part had been able to lean on defense while the team went through personnel upheaval, including the suspension of starting center Joshua Smith for academic reasons and starting guard-forward Jabril Trawick’s broken jaw.

Georgetown offered glimpses late in the season it belonged at least in the discussion for the NCAA tournament with victories over Xavier and then-No. 13 Creighton. Those wins against two of the top four teams in the Big East came by an average of 17 points, underscoring the Hoyas’ predilection to dramatic bouts of inconsistency.

“We really need to string a couple wins together,” senior forward Nate Lubick said. “It’s very, very important, and we know that. Like I said, we play DePaul next, and beating DePaul and getting to the next game is what’s most important right now.”