WASHINGTON — Donnie Quixote awakened from his season-long dream on Thursday night.

He sounded exhausted, if not defeated. Reality had set in.

The Dodgers’ endearingly optimistic manager made an uncharacteristic concession in the wake of a crushing 4-1 defeat to the Washington Nationals on Thursday night: The season felt as if it was slipping away.

“Honestly, it does,” Don Mattingly said. “I just don’t think there’s any way for us to look at it other than that.”

This was the same man who downplayed the obvious gaps on his roster in spring training and went as far to try to portray them as potential strengths. He insisted that his club could continue to win games in May as he filled out lineup cards that looked straight out of triple A. Even as the Dodgers tumbled down the standings in recent weeks, he maintained his calm.

With only 12 games remaining in their season, the Dodgers are three games back of the St. Louis Cardinals for the second of two National League wild-card spots. The Milwaukee Brewers have also passed L.A. in the wild-card standings.

Winning the NL West is out of the question. The San Francisco Giants’ magic number to claim the division title is down to three.

These Dodgers, with their big-money additions, were supposed to make history. Instead, they witnessed it Thursday, as the Nationals became the first Washington-based baseball team to clinch a playoff berth since 1933.

The Dodgers’ next series will be in Cincinnati against the NL Central-leading Reds, who, hours before the Nationals’ win, became the first team in baseball to secure a place in the postseason.

Mattingly had refrained from ever saying his team had to sweep a series. That changed after the Dodgers’ second loss in a three-game series with the Nationals.

Mattingly said the Dodgers have to win all three games in Cincinnati.

“I think we have to think like that, like we need to,” he said.

Mattingly acknowledged that he sensed discouragement among his players.

“I think guys are discouraged a little bit because things just haven’t gone the way we want things to go,” he said.

The players disputed that.

“The energy’s there,” shortstop Hanley Ramirez said.

The Dodgers were held to four hits, including three over the first six innings given up by Nationals starter Ross Detwiler.

Matt Kemp and Adrian Gonzalez were each one for four. Ramirez was hitless in four at-bats. Andre Ethier was 0 for 3.

The Dodgers’ only run came on a fourth-inning home run by Mark Ellis.

Ellis was confounded by the team’s continued offensive struggles.

“We answer that question every day,” he said. “I don’t think anybody can put a finger on why we’re not scoring runs. We don’t know what it is.”

Dodgers starter Chris Capuano dropped to 1-6 over his last 10 starts. The left-hander was charged with four runs (three earned) and four hits in five innings.

The Dodgers’ pitching is far from awful these days, but it’s nowhere near what it has to be to overcome the offense’s meager production.

With Chad Billingsley lost for the season to an elbow injury and Clayton Kershaw sidelined indefinitely with a hip problem, the Dodgers don’t look like they will be shutting out the opposition any time soon.

Mattingly now faces the increasingly difficult task of inspiring himself before he can inspire his players.

“It’s been challenging because you have to continually pick yourself up and push your club to get better and to keep fighting,” he said. “That gets tougher and tougher as games dwindle away and you fall back. It’s a challenging time.”

dylan.hernandez@latimes.com