The Giants had previously mounted their own four-run ninth-inning comeback in Friday's 5-4 series opener and survived the A's four-run rally at the end of Saturday's 9-8 win, but couldn't hold on Sunday for the series sweep.
"You have to learn pretty quick whether it's a big win or a big loss to just move on to the next and continue playing the game hard," catcher Buster Posey said.
Norris drove a chest-high fastball into the left-field seats off closer Santiago Casilla, erasing the Giants' previous 2-1 advantage with his first career home run.
"He had a couple mistakes early," Bochy said of Casilla. "I think he was a little hyped up there at the end. Occasionally you can have a hiccup and leave the ball up. This is all part of being a closer."
After a curveball in the dirt to begin the at-bat, Casilla went with six straight fastballs to Norris, but Posey brushed off any second thoughts about the pitch selection in Casilla's second blown save of the season.
"Hindsight is always 20/20," Posey said. "Of course I think about it and Casilla thinks about it, too. But he's a fastball pitcher, and you have to give the hitter some credit, too."
The ninth inning erased what had been yet another strong performance from starter Matt Cain, who turned in a seven-inning, one-run performance in which he held the A's to three hits while striking out seven.
"Today's definitely tough," Cain said. "It's definitely not a good feeling, but we have to put it past ourselves and worry about tomorrow."
The loss ended Cain's career-best eight-start winning streak, marking the first time he has not picked up a win since May 6.
"We've been playing good baseball and just couldn't squeak a couple wins out, battled back last night," Norris said. "Today Cain pitched very well. It was very tough to scratch any runs off him, but we battled back and got a 'W.'"
Before the ninth inning, the game's scoring had come in the first inning. Oakland's A.J. Griffin struck out Gregor Blanco to start the right-hander's Major League debut before going on to give up a single to Ryan Theriot, who scored two batters later when Posey went deep for his 10th home run of the season.
The A's responded in their half of the inning when Josh Reddick singled home Coco Crisp, who had doubled down the right-field line to start the game.
"I just made a bad pitch to Crisp in the first inning," Cain said. "One of those mistakes you don't want to make, and it just happened to be in the first inning and cost us a run."
From there, Cain settled in, retiring 13 straight batters at one point. The A's looked to have been on their way to getting some runs on Cain in the sixth when Seth Smith lined a pitch deep down the right-field line with runners on first and second, but the play was ruled a foul ball. A's manager Bob Melvin came out to argue the call with first-base umpire Todd Tichenor, and TV replays appeared to show that he might have had a case.
"I didn't have a great look at the ball, but to me, it looked just foul," Cain said. "The umpires had a better look at it than I did."
Cain got Smith to foul out to left fielder Melky Cabrera after battling through the 12-pitch at-bat and threw a perfect seventh inning before departing.
"He threw the ball great," Posey said. "Cain did a great job of staying consistent. He's just been doing what he's done all year, throwing all four pitches when he's wanted to."