The game was tied at 3 when the Dodgers scored the go-ahead run off right-hander Miguel Batista in the top of the 13th inning.
With two outs and Rafael Furcal on second, Russell Martin hit the ball to center field and it looked like Morgan had a bead on it, but the ball bounced in front and away from him as Furcal scored easily to give Los Angeles the one-run lead.
"I was just aggressive at it. I was coming after it tough," Morgan said. "I wanted it to stay up for me. But it was sinking quick. It's one of those things where I mistimed it, but I really wanted to keep it in front of me."
But Washington didn't go down quietly against reliever Carlos Monasterios in the bottom of the inning. With one out, Ivan Rodriguez, who sat out most of the game because of tightness in his back, singled to right and advanced to third on a single by Morgan.
Ian Desmond came to the plate and hit a slow roller to third baseman Casey Blake, who threw out Rodriguez at the plate. Rodriguez argued with home-plate umpire Brian O'Nora, but after looking at the replay, Rodriguez said O'Nora made the right call.
"I went in and saw the replay and I was out probably two or three inches. He made a good call," Rodriguez said.
The game came to an end when Cristian Guzman flied out to left fielder Xavier Paul.
Nationals manager Jim Riggleman came away feeling that his team played well.
"I thought we played real good baseball," Riggleman said. "We got some timely hits. Pitching was good. It was a pitching and defense game. I wish we could have gotten the runs in. It just didn't happen."
Right-hander Craig Stammen had his second straight quality start, but didn't figure in the decision.
Stammen lasted seven innings and gave up three runs on six hits, but it was the long ball that did him in. The Nats were ahead, 1-0, when Blake hit a two-run homer to give Los Angeles a 2-1 lead in the top of the second inning.
But Stammen tied the score in the bottom of the sixth inning when he drove in Alberto Gonzalez with a single to center. It looked like the Nationals would score the go-ahead run in the same inning. Morgan came to the plate and hit the ball over Paul's head in left field. It looked like Stammen was going to score easily, but Morgan was thrown out at third base to end the inning before Stammen touched home plate. The game remained tied at 2.
Morgan admitted that he made a baserunning mistake. He should have stayed at second or gotten into a run-down play.
"I was being aggressive, but not intelligent," Morgan said. "But my thought was they were trying to [throw out] Stammen. I should have stopped about halfway, but I was locked in. I had tunnel vision there and didn't understand the situation a little bit. I have to be smarter in that situation. It was an aggressive play. I was thinking they would throw out the pitcher instead of trying to get me at third. I should have known better not to make the last out at third base."
Third base coach Pat Listach said Morgan simply made an aggressive mistake.
"You don't want to make a mistake there -- the first or third out at third base or the first or third out at home plate," Listach said. "That was a situation where he hit the ball over the left fielder's head. Nyjer has to realize and make sure that the pitcher scores before he gets tagged out."
The second run was charged to Dodgers left-hander Clayton Kershaw, who lasted six innings and gave up two runs on eight hits. But it looked like he would be the winning pitcher when Blake hit his second home run -- a solo shot -- off Stammen in the top of the seventh inning.
"My outing was OK," Stammen said. "I made some mistakes that cost me some runs. But I made some good pitches. They got guys on first and we got a couple of double plays. The defense did real well and [catcher] Wil Nieves did real well behind the plate."
The Nationals ended up tying the score in the bottom of the eighth inning. With Dodgers closer Jonathan Broxton on the mound, Adam Kennedy stole his fourth base of the season and advanced to third on a throwing error by Martin. Kennedy then scored on a single by Morgan.
But the Nationals ended up losing the game as they dropped their record to 9-9 for the young season.
Bill Ladson is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.