Muncy owned up to a significant throwing error that led to three gift-wrapped runs in the sixth inning with right-hander Jesse Chavez on the mound.
Salvador Perez, who would later break open the game with a two-run homer off Edward Mujica in the eighth inning, grounded a chopper to Muncy with one out and runners at the corners. Muncy, already gravitating toward home, threw the ball over the head of catcher Stephen Vogt, giving the Royals their first run and allowing two of their men to reach second and third.
That's when the A's opted to load the bases, intentionally walking Alex Gordon, to get to a pair of right-handed hitters in Alex Rios and Omar Infante for a ground ball. Rios hit a sacrifice fly to deep center, and Infante followed with a base hit, tying the game.
"I just rushed myself," said Muncy, who was making his first start at third base in place of a resting Brett Lawrie since June 16. "I had plenty of time and I rushed myself and made a bad throw on it.
"When your name is called you need to go in there and make the play. That's all there is to it."
Chavez, who was charged with three earned runs in 5 2/3 innings, was insistent on taking the blame.
"I gotta stop the bleeding and make a pitch," Chavez said. "It didn't go our way. I made a pitch to the next hitter for what would have been the third out.
"There's no excuse for it. It's all my fault."
Muncy's miscue was the A's 74th of the season. Their 75th, 14 more than any other team, came in the ninth, when shortstop Marcus Semien bobbled a groundball for his 23rd error.
The A's finished their season series with the Royals, 1-5, and while this weekend proved less contentious than April's benches-clearing matchup, it was just as disappointing for a club that was just starting to click on all cylinders.
"We had a good thing going," Chavez said, "and then we hit a bump to start our homestand. It's something we don't want to do."
• Josh Reddick fouled a pitch off his right shin in the third inning, but remained in the game and proceeded to pop up a ball in shallow left field that dropped in for an RBI single, marking his 500th career hit.
• Billy Burns was back in center field, after missing two games because of a hip flexor issue, and finished with two hits, extending his hitting streak to a career-high 16 games -- the longest by an Athletic over the last five years.