Lester had won his last seven decisions, but the left-hander's focus was on the team's sudden downturn.
"Guys are competing, we just aren't getting results right now," he said.
"The times that we need to get a guy in, we're just not doing it. The times we need to make a pitch, we're not doing it. This team's too good to stay in this funk."
The A's have lost seven of eight overall and trail the Angels, who lost to Texas on Sunday, by percentage points in the AL West. Before Saturday's loss, Oakland had been alone in first place since April 28.
"This is really the first bad road trip we've had this year," Oakland manager Bob Melvin said. "This was not a good trip. So we've got to get home and we've got to regroup. It will be good to get home in front of our crowd. They're usually good for us."
Oakland's Nate Freiman hit two homers, giving him three in the series, but Minor allowed only two other hits.
Craig Kimbrel worked a perfect ninth for his 37th save.
Lester (13-8) allowed four runs, three earned, and six hits in six-plus innings in his first loss since June 7 for the Red Sox at Detroit. He had been 3-0 with a 2.49 ERA in three starts since his July 31 trade to the A's.
Phil Gosselin led off the Atlanta fourth with a single to right field. With one out, Upton drove a low, inside pitch from Lester about 10 rows deep into the left-field seats for a 3-1 lead.
"I thought it was a good pitch when I threw it," Lester said. "I went back and looked at it and, good pitch. So sometimes you've got to tip your hat."
Upton hit four homers in the 10-game homestand, including two against the A's. He has hit 16 of his 23 homers at Turner Field.
Lester is still waiting for his first career hit. He was 0 for 34 in eight seasons with Boston and his drought continued in his first two at-bats with the A's. He struck out and hit a fly ball to left field.
Oakland hasn't had a six-game losing streak since losing nine straight from May 22-June 1, 2012.
Athletics: CF Craig Gentry, on the 15-day disabled list with a broken right hand, is ready to begin a rehab assignment with Triple-A Sacramento.
Braves: Gonzalez said RHP Shae Simmons (strained right shoulder) will make a second rehab assignment with Triple-A Gwinnett on Monday after throwing 10 pitches without a problem on Saturday.
Athletics: After an off day on Monday, the A's take on another NL East team when they open a two-game series against the New York Mets on Tuesday night. Scott Kazmir (13-5), who already has matched his career high in wins, will start for Oakland.
Braves: After completing their 10-game homestand, the Braves open a series at Pittsburgh on Monday night as RHP Ervin Santana goes for his 13th win. Santana (12-6) leads the Braves in victories.