The Braves won for just the fifth time in 13 games, pushing their NL wild card lead over St. Louis to three games with just five to play. The Cardinals lost to the Chicago Cubs on Friday.
"We don't have many games left and we have to take care of our business over here and then worry about whatever happens with them," said Uggla.
Strasburg (0-1) got his first decision in four major league starts since coming back from Tommy John surgery, but it was a losing one.
He settled down after a shaky first inning but came out of the game after four innings -- the fourth straight time since his return that he pitched six innings or fewer.
Tim Hudson (16-10) improved to 14-3 lifetime against the Nationals franchise despite lasting just 5 2/3 innings and giving up three runs on nine hits.
Jayson Werth hit a solo home run for the Nationals, who were coming off a four-game sweep of the NL East-champion Phillies.
Entering the game, Strasburg had allowed only two runs in 14 innings in his three previous starts, striking out 11 and walking none.
But the 23-year-old right-hander labored through a 38-pitch first inning in this one, taking the mound after a 14-minute delay because of heavy rain before the game.
Nationals manager Davey Johnson, who wanted Strasburg to throw around 80 pitches, thought starting the opener of a three-game series against a team fighting for the postseason may have affected the youngster's mind set.
"I've had that conversation with him about going down there and just letting what happens happen. But I think the moment got him geared up and it was kind of hard for him to settle down."
After striking out leadoff hitter Michael Bourn, Strasburg gave up three consecutive singles to Martin Prado, Chipper Jones and Uggla to score the first Braves run. He fanned Brian McCann, but Freddie Freeman followed with an RBI single to make it 2-0.
The last run was unearned after the normally sure-handed Ryan Zimmerman let a sharp Jack Wilson grounder get past him at third base. Strasburg threw 23 of his 38 pitches for strikes in the inning, but struggled with his command.
"That was not typical him," Johnson said. "He was throwing more than he was pitching and his location isn't as good when that happens."
The Nationals got within 3-1 in the second inning when Danny Espinosa doubled and scored on Wilson Ramos' single.
Strasburg threw 75 pitches in the game, including 46 for strikes, and only allowed one more baserunner after the first inning -- Uggla's single in the third -- before he was relieved by Collin Balester to start the fifth.
Atlanta pounced on the new pitcher, scoring three more runs to take a 6-1 lead. Bourn drew a leadoff walk and stole second base before Jones reached on a one-out walk. Uggla's double plated Bourn and knocked Balester out of the game for Atahualpa Severino, who surrendered McCann's two-run double to the right-center field wall.
Michael Morse hit a one-out double in the sixth and scored on Werth's single to start a two-run rally. Espinosa followed with a base hit and both runners moved up on a ground out before Ramos' single scored Werth to get the Nationals within 6-3.
In the eighth, Werth belted a 3-2 pitch from Jonny Venters over the wall in left field for his 20th homer of the season.
The Braves scored their last run on a weird series in the ninth inning, when Bourn sprinted home with no one covering the plate as the Nationals had Jones in a rundown between first and second base. At one point during the play, Bourn and Jones were both headed to second base from opposite directions.
Craig Kimbrel earned his 46th save for Atlanta, striking out two batters with a runner on base.
The Nationals fell to 10-3 in their last 13 games. They are 1-3 in Strasburg's four starts this season...Hudson has earned a decision in seven straight starts (4-3) since his last no-decision on August 15.