Nationals starter Zach Duke walks to the dugout after being relieved in the fourth inning. (John G. Mabanglo/EPA)

The goal for the Washington Nationals remains unchanged, and if they overcome the bewildering first portion of their season to reach it, they may look back on Monday night and wonder: how did they ever get so lost on the way to the World Series?

When the Nationals gathered in spring training and the baseball world anointed them favorites, they could not have envisioned something like the 8-0 slog they endured at the hands of the defending champion San Francisco Giants. Two long relievers, Zach Duke and Craig Stammen, formed an ineffective fill-in starter. Their offense succumbed to an opposing starter who carried an 8.06 ERA to the AT&T Park mound. They were out-hit, 17-3, and their overall record, with a third straight loss, dropped to 23-22.

Monday night, a day after the San Diego Padres drubbed them by nine runs, represented a low point even before the surreal revelation that followed: Reliever Ryan Mattheus had punched his locker Sunday afternoon after allowing the Padres five runs in one inning. Monday afternoon, Mattheus and the Nationals learned he had broken his right hand — his throwing hand — and would be placed on the disabled list.

“It’s pretty embarrassing,” Mattheus said. “I let the whole Washington Nationals organization down by doing something stupid.”

A pitching staff already in disarray called in reinforcements for Tuesday. The Nationals sent down outfielder Eury Perez and called up left-handed reliever Fernando Abad and right-hander Yunesky Maya to fill out an over-taxed bullpen.

“Today,” Manager Davey Johnson said, “was awful tough.”

With Ross Detwiler shelved with an oblique strain, Johnson gave Duke his first major league start since July 2011. He last 31 / 3innings and allowed seven hits before he yielded to Stammen. The Giants kept mashing, pushing across two runners Stammen inherited and adding one more on Brandon Belt’s mammoth solo homer in the fifth.

The Nationals’ lineup, meantime, floundered again. Sinker-balling right-hander Ryan Vogelsong staggered into his start having not reached the fifth inning since April. He shut the Nationals out for five innings, allowing three hits and leaving only after a fastball fractured his right hand during an at-bat. Four Giants relievers faced the minimum over the final four innings. The Nationals entered with a .292 on-base percentage, and it fell to .289.

Monday afternoon in the visitors’ clubhouse, the Nationals had held the hitters’ meeting that accompanies the start of every series, a gathering for the purpose of reviewing the opposing pitching staff. This meeting was not routine. Shortstop Ian Desmond and third baseman Ryan Zimmerman, the two players with the longest tenures in Washington, spoke up.

Following the loss, Zimmerman provided to reporters only an abridged version of his message: “Relax and play,” he said. Desmond focused on the idea that every hitter, like last year, needed to use the individual that brings them success.

“When things don’t go good, it’s easy to point the finger,” Desmond said. “I just wanted to express to the guys, hey, do what you do best. That’s all we can ask. If everybody does the best job they can, at the end of the day we’re going to be a pretty good ball club. Right now, it takes hitting, pitching and defense to win ballgames, and we’re doing one of the three sporadically. There’s no doubt in my mind it’s going to turn around. But at this point, it’s starting to get a little bit frustrating. At the same time, this is a long season. This is not a game for the mentally weak.”

By night’s end, the Giants were resting regulars and showing mercy — Hunter Pence pulled up short rather than slide on a play at the plate in the seventh. The Nationals have shown a proclivity for getting blown out this year. In five games, they have lost by at least seven runs.

“Anytime you underperform or don’t do what you’re supposed to do, it’s frustrating,” Zimmerman said. “That’s not going to do us any good tomorrow. We just have to come out and keep working and know that by the end of the year, things will kind of even themselves out. The minute you start feeling bad for yourself or start hoping someone else does it, that’s when trouble happens.”

How far off course are the Nationals? To equal last year’s 98 wins, the Nationals would have to reel off a 75-42 run from now until the end of the season. Their offense holds the brunt of the responsibility. Last year, Washington scored 4.51 runs per game. After their sixth shutout in 45 games, the Nationals are averaging 3.44 runs this year. In order to match last year’s offensive output, the Nationals would have to score 4.92 runs per game the rest of the way.

“I like the team we have,” General Manager Mike Rizzo said Sunday morning, eschewing the need to add a bat. “I like the offense as it is. We certainly need more production from certain parts of the lineup. We need a more consistent lineup. We need a healthier lineup. But everyone has injuries, and we need to play through them. Guys need to step up and perform in the absences of our regulars.”

Monday, not even Bryce Harper’s return to the lineup after he missed two games, one week after he crashed into the wall at Dodger Stadium, could lift the Nationals. Harper went 0 for 4 with a strikeout.

Harper moved well in right field, and the pesky Giants provided him, and the rest of the Nationals’ defense, with plenty of action. Duke took the mound excited for his cameo in the rotation, back to the role in which he spent the majority of his career. He missed few bats.

The Giants first got to him in the second inning. Pence and Belt knocked consecutive singles, and Andres Torres roped a double to left. After an RBI groundout, the Giants led, 2-0.

Duke pitched out of a jam in the third, but the Giants struck again in the fourth. Belt and Torres led off with consecutive base hits. Crawford smoked a liner back at Duke, which he knocked down for an out, but Johnson had seen enough.

Johnson pulled Duke with one out in the bottom of the fourth inning, a curious moment to make a change. Vogelsong, the opposing pitcher, stood at the plate, so the batter posed no imminent threat. For the Nationals, the pitcher’s spot was due up fourth in the top of the fifth inning. Still, Johnson turned to Stammen.

Vogelsong greeted Stammen with a safety squeeze bunt. Belt crossed home plate to give the Giants a 3-0 lead. The Nationals still had five trips to the plate remaining, but the game felt close to over. Their sputtering offense had not come back from a deficit of larger than two all season.

Stammen, highly effective all season, could not limit the damage. He promptly allowed a double to Angel Pagan and a single to Marco Scutaro. Like that, the Nationals trailed, 5-0, and Duke’s ERA had risen to 8.84. The Nationals signed him in early December to a major league deal worth $700,000.

The remainder included more ignominy. The only base runner the Nationals managed off San Francisco’s bullpen was immediately erased by a double play. Henry Rodriguez threw 30 pitches in the seventh inning and, despite the fact that he had thrown an inning Sunday, he stayed out and pitched the eighth, too. By the time he finished, Rodriguez had thrown 68 pitches over the past two days, and Tyler Clippard was warming in the bullpen.

The bleak tableau was complete. Bullpen reinforcements were on the way. One of their top set-up relievers packed for home, his hand mangled. Seagulls circled above the stadium. Happy fans filtered out, and a lost team walked back to the visitors’ clubhouse.

“We have some guys that are underperforming,” Zimmerman said. “It’s still early. But obviously, in the middle of May, you hope to start getting the ship going the right way. There’s no use sitting here and complaining about it. You got to go out there and make a change.”