Years from now, there will be few reasons to remember a game that was played in a steady rain, in front of a few thousand fans, for a result that determined nothing more than the passing of time.

It was an ending, if anything, to a miserable and forgettable season — and, as it is expected, to Mike Shanahan’s time coaching the Washington Redskins. He said he’ll meet with team owner Daniel Snyder on Monday morning to decide his fate.

“It’s not a fun profession,” Shanahan said, “when you lose.”

There hasn’t been much fun this season, then, and the only thing that made the Redskins’ 13th loss unique — even more so than the seven that came immediately before it — was that there’s no chance of more disappointment next Sunday. This is the end, a 20-6 New York Giants victory that’ll be a footnote even in local history, and in the locker room, there seemed to be some relief in that. The hope of a promising season disappeared weeks ago; the optimism of returning a broken franchise to the tracks in 2013 dissolved during one of the most turbulent months in the history of a franchise now most famous for instability.

Before the game, a time reserved on recent Sundays for leaked reports, the expectation was that Shanahan would be fired. The only question was when. Afterward, Washington’s locker room wasn’t somber or quiet; it was jovial. A few players shook off the final shivers once inside the warmth. Running back Roy Helu Jr. stood at his locker and sang. Safety Brandon Meriweather and wide receiver Pierre Garcon stood near the showers and laughed. A few minutes later, Meriweather and fellow defensive backs E.J. Biggers and Trenton Robinson sat at their stalls and joked, smiling like players do after wins and winning seasons.

Not everyone saw reasons to celebrate.

“I don’t think anything is funny about it,” fullback Darrel Young said. “It’s all negative.”

Shanahan was hired to bring meaningful football to the end of Redskins seasons. Games during the schedule’s final week were supposed to decide playoff seeds and home-field advantages. Instead, Shanahan ushered in three losing seasons out of four, with the 2013 season bringing the highest expectations and the most devastating reality.

If this is the end of the Shanahan regime in Washington, the final scoring drive of a coach once considered an offensive genius was sloppy and forgettable. It finished with Kai Forbath’s 49-yard field goal to end the first half, the payoff after Josh Wilson’s interception of Eli Manning. Washington quarterback Kirk Cousins moved his team for one first down before Forbath’s kick, and that’s how Shanahan’s team scored its last points of 2013 — and maybe the final points of a once-impressive career that had the coach on the fringe of the Hall of Fame.

Instead, a crossroads season and tenure for Washington ended in the slop, with bad passes, bad punts, bad ball security and bad defense. The Giants scored a touchdown on a 49-yard run, their longest of the season. There were drops and tipped passes and near-interceptions, a combined seven first-quarter punts. It was slip and slide, meaningless and unmemorable fun in the chilly Meadowlands.

“I want to forget,” said linebacker Brian Orakpo, who didn’t play Sunday because of an injured groin and will be a free agent. “I don’t ever want to remember a three-win season.”

If there was one lingering fact, it was that Cousins, elevated to starter three weeks ago to replace the deactivated Robert Griffin III, hurt any perceived trade value entering what’ll almost definitely be an offseason of widespread change. Shanahan wondered aloud this month whether Cousins could attract a first-round pick in a trade if he played well enough in Washington’s final three contests. Throughout Sunday’s game, that prospect seemed laughable. Cousins completed 19 of 49 passes , was sacked three times and threw two interceptions. He watched as only Giants defenders’ unsure hands prevented several more picks. Cousins also lost a fumble.

“Today,” Shanahan said, “was a rough one on everybody.”

This was another game, like many before it, in which Washington’s defense gave it little chance to win. Even after Manning left at halftime with an ankle injury, the Redskins couldn’t stop his replacement, Curtis Painter, or a running game that, at one point this season, had the Giants 0-6 and the favorite to finish last in the NFC East.

That distinction now belongs to Washington, a familiar habitat, even a year after it won seven in a row and ended the season with a home win against Dallas to capture the division title.

Although the faces Sunday were mostly the same as those celebrating at FedEx Field last December, that seems like a long time ago. And in the NFL, games and seasons like this lead to changes. That’s an inevitability now.

“We’ve had some good times,” Young said, a moment before lamenting that at least most players stayed healthy.

Who will return and try to clean up this mess, on the roster and, increasingly likely this past month, in the coaching offices? Will Cousins’s performance make him so unattractive a trading chip that the Redskins simply hang on to the 2012 fourth-rounder, beginning another offseason of debate about Griffin’s comfort with Cousins in the same locker room?

Shanahan was brought here to answer questions, not create more of them. He was hired to bring on locker-room celebrations, sure, but not after the final game of a 3-13 season — the franchise’s worst record since 1994.

Meriweather, after leaving his locker, temporarily quieted his laughter when approached for a question. No, he wasn’t happy or relieved, he said; he is a competitor.

“You always want to win,” he said before walking toward the exit, joining several teammates, and a moment later they were again loud and smiling, shaking off what they’d just experienced like a group of men coming in from the cold.