Kazmir (4-5) pitched well overall, allowing three runs on seven hits in seven innings, and commanded the ball effectively for the most part.
A few specific plays cost Kazmir in the loss, and the Royals capitalized en route to a series-clinching win.
"We've been playing great baseball the past couple weeks," Kazmir said. "To fall two straight like this to a team like that is tough."
The first game-changing play came in the third inning, when Kazmir was called for a balk. Omar Infante advanced to third, and Mike Moustakas hit a sacrifice fly to knot the game at 1.
A's manager Bob Melvin doesn't believe Kazmir did anything wrong.
"I didn't see a balk," Melvin said. "To me, he stepped off. That's a big run."
Kazmir said home-plate umpire Fieldin Culbreth believed Kazmir started his delivery. The left-hander told Culbreth he was simply stepping off to talk to catcher Josh Phegley, but Culbreth saw it differently.
Melvin emerged from the dugout to make sure Kazmir stayed in the game, which he did.
"It's a tough call," Kazmir said, "but you battle through it."
After two straight scoreless innings, Kazmir struggled in the sixth. Lorenzo Cain and Eric Hosmer moved to second and third on a double steal that Kazmir said he should have seen coming.
"That could have been the difference between one run instead of two," Kazmir said. "Little things like that could have been the difference in the ballgame."
Both runners scored when Kendrys Morales delivered the game's biggest hit -- a two-run single to right. Kazmir said he thought he pitched great overall, but that was the one pitch he regretted.
He tried to jam Morales with a cutter, but the ball ended up hovering over the plate.
The A's struggled to capitalize on offense as well. Sam Fuld and Brett Lawrie led off the eighth with walks against Wade Davis, who entered with a 0.29 ERA. But Stephen Vogt struck out and Ben Zobrist hit into an inning-ending 1-6-3 double play to squelch the rally.
"We had first and second with nobody out and the meat of our order, guys we feel great about," Melvin said. "We just didn't get a big hit there."
Trevor Hass is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.