Doug Slaten came in to replace Clippard with runners on first and third and Juan Uribe at the plate. Slaten then gave up a two-run double to Uribe to make it 8-5.
The Nationals are now 39-49 on the season.
"The Giants had a lot of great at-bats against him, but Tyler's just struggling," Nationals manager Jim Riggleman said. "I don't know what else to say. He has had so much success getting hitters to swing at his fastball that's up around there, letter-high.
"Right now he's throwing it a little bit lower in the hitting area or a little bit too high to get them to offer at it. That's been a real good pitch for him to get strikeouts and that's not been happening. He's just a little off. He's just struggling and he's going to have to go out there and figure it out."
Clippard hasn't been able to figure it out lately. In his last seven appearances, he has three losses and has given up 13 runs on 15 hits.
Nationals pitching coach Steve McCatty said he noticed a few differences in Clippard since earlier in the season.
"Now the ball is up a little more," McCatty said. "The changeup is not consistently down and he's just not making pitches. Obviously he's in a rut right now. It looks to me like he's overthrowing a little bit."
Clippard left before the media were allowed in the clubhouse.
The Nationals didn't look like they would need bullpen help early, though, as their offense scored five runs in the first four innings.
Washington starter Craig Stammen did well at times and earned a no-decision after allowing four runs on six hits in 5 1/3 innings. He also hit an RBI double to center field off Jonathan Sanchez (2-2) to give the Nationals a 5-3 lead in the fourth inning.
"That's one thing I try to bring to the table," Stammen said. "I'm going to battle no matter what I'm doing. He made me a bad pitch, just like I threw him a bad pitch, so I returned the favor, I guess."
Ryan Zimmerman got an RBI double off Sanchez in the first inning to put Washington ahead, 1-0. Two batters later, a wild pitch allowed Cristian Guzman to score from third base. Michael Morse added a solo home run in the second inning.
But once taking a 5-3 lead in the fourth inning after both Ivan Rodriguez and Stammen hit RBI doubles off Sanchez, Washington's bats went cold. The Nationals had only three hits from that point on. In fact, Washington's last 10 batters were all retired in order.
The Nationals had good scoring chances in the fifth and sixth innings, but couldn't add any runs. They had the bases loaded in the fifth, but Rodriguez grounded into a force play. In the sixth, Posey threw out two runners at third base, one on a bunt and one on an attempted steal.
Riggleman said those failed opportunities were a factor in the loss.
"We had an offensive night, it looks like," Riggleman said. "You score five runs, but there was more out there that we didn't get. It came back to bite us."