D.C. United Coach Ben Olsen, shown earlier this season, is likely to be back next season even though the team set a league record for fewest victories in a season. (John McDonnell/THE WASHINGTON POST)

D.C. United etched itself into MLS history again Sunday, but on this glum occasion at RFK Stadium, there were no trophies nor celebrations involved. As the final whistle sounded in a 2-1 defeat to the Houston Dynamo, the league’s most decorated organization began to come to terms with setting the record for fewest victories in a season.

March 9, June 22 and Aug. 3 — the dates of United’s only triumphs across an eight-month, 34-match campaign. Tampa Bay (2001) and Chivas USA (2005) won four times in 27 and 32 games, respectively.

United (3-24-7, 16 points) finished on a 12-game winless streak, and if not for Kyle Porter’s header in the first half against the playoff-bound Dynamo (14-11-9, 51), D.C. would have tied its own league mark for fewest goals (21) set three years ago.

It scored multiple goals just three times and became the fifth team to go winless on the road. The public continued to lose interest: Average home attendance was the smallest in club history (13,646), eclipsing the mark set last year. The finale drew 13,731.

United’s only joy: winning the U.S. Open Cup, a century-old tournament involving amateur and pro teams. “I’m glad we won the Open Cup,” goalkeeper Bill Hamid said, “but that record, man, I’m sorry, it sucks.”

A year ago, United finished with the third-most points in the regular season and advanced to the Eastern Conference finals. Ben Olsen received votes for coach of the year, Chris Pontius was an all-league selection, Nick DeLeon was a rookie of the year finalist and the back line was among the league’s best.

Now, management will have to decide whether to retain Olsen and General Manager Dave Kasper, whose contracts are guaranteed next year. It will have to sift through the roster, determine whether to offer captain Dwayne De Rosario a new contract, and prepare for the first picks in multiple drafts and other platforms.

“Next year is going to be even tougher,” said De Rosario, referring to United’s place in the CONCACAF Champions League, an international competition. D.C. earned a berth by winning the Open Cup. “A lot of things need to change.”

Jason Levien and Will Chang, two-thirds of the ownership group, attended Sunday’s match. Levien, who speaks on the investors’ behalf, said he did not want to comment on the club’s plans. Sources close to the situation said a few weeks ago that the club is likely to retain Olsen and probably keep Kasper.

Asked if he expects to keep his job, Olsen said: “It’s not up to me, but I am preparing and doing everything I can to make sure we are ready for next year, whether that’s the case or not. . . . We understand what we need, we understand how we want to go forward and the type of players I need. It’s real: We’re not good enough.”

United displayed that again Sunday. James Riley, a left back playing center back, took down Giles Barnes from behind, leading to Oscar Boniek Garcia’s penalty kick in the 11th minute — the 23rd goal conceded by United in the first 30 minutes.

United equalized in the 27th when Pontius served an end-line cross to Porter for a back-post header. After United’s two-man breakaway failed to place a shot on target, Hamid made outstanding saves on consecutive shots. On the ensuing corner kick, however, poor marking allowed Barnes’s glancing header in the 39th minute.

In the second half, United’s penalty pleas were ignored, Hamid made another terrific save and D.C. faded into what promises to be a tumultuous winter.

“Not enjoyable,” Pontius said of the season. “Not an enjoyable one.”

REVOLUTION 1, CREW 0: Juan Agudelo scored midway through the first half as New England defeated host Columbus and qualified for the postseason for the first time since 2009.

The Revolution needed to win after Houston’s win to also reach 51 points.

“It’s a credit to all our guys because it wasn’t the prettiest game,” Revolution Coach Jay Heaps said. “They showed a lot more heart than any game I’ve seen because there were situations we had to fight and dig in deep.”

RED BULLS 5, FIRE 2: Peguy Luyindula had three assists to help host New York defeat Chicago and finish with the league’s best regular-season record.

Ibrahim Sekagya scored early in the second half to help the Red Bulls get to 59 points for the regular season, lifting them over Sporting KC, which had 58 points.

Real Salt Lake led the Western Division with 56 points.

It’s the first Supporters’ Shield for the Red Bulls.

WHITECAPS 3, RAPIDS 0: In Vancouver, Camilo Sanvezzo scored three times against Colorado to give him an MLS-best 22 goals.