The D-backs have now lost five of their last six games.
"We got outplayed," D-backs manager Kirk Gibson said. "But we've got to move on."
Nuno (0-3) lasted just four innings as he allowed five runs on seven hits. He did not walk a batter and 43 of his 57 pitches went for strikes.
The Royals, though, did not let him get away with mistakes made out over the plate and jumped on fastballs early in counts.
"Ball was up," Gibson said. "You see a lot of balls in the air, even his outs were balls that were hit pretty good in the air. That's why I got him out of there early. I was kind of trying to hang on and get as many innings out of him as I could, but he gave up five runs.
"If he doesn't keep the ball down, he's not going to be effective, just like every other pitcher who does that as well. He didn't have a lot of movement today, he wasn't throwing to both sides of the plate, he wasn't keeping the ball down, that's tough, a tough way to go."
The D-backs actually gave him a lead in the first when Mark Trumbo's sacrifice fly scored Ender Inciarte. It did not last long.
Billy Butler led off the Kansas City second with a double and Alex Gordon hit a first-pitch fastball for a two-run homer.
One inning later, the Royals took a 4-1 lead when Salvador Perez grounded a two-run single down the left-field line.
"I was leaving the ball up," Nuno said. "They found a way to get the ball in play and, sure enough, they scored five runs. It was a mental thing, a little bit."
Adding to his frustration was the fact that Nuno knew what he needed to do to get back on track, but he was unable to execute.
"It was just balance and release point," Nuno said. "My release point was kind of high today. In the back of my mind every inning or every pitch I threw, I was like, 'I've got to drive a little bit more,' or 'I've got to let it go a little bit longer.'"
Royals starter Jeremy Guthrie (8-9) was not sharp at the outset as he allowed seven hits in the first three innings.
However, much like Wednesday night when they went 2-for-14 with runners in scoring position, the D-backs were not able to capitalize on their opportunities.
The D-backs managed two runs over the first three frames, but left five on base.
"We were swinging the bats good the first three innings, we had a lot of opportunities," Gibson said. "Didn't capitialize as much as we could have, got only two runs out of that. And then he shut us down after that, so tough sledding."
They would not get any further chances against Guthrie, who did not allow a hitter to reach after the third, retiring the final 19 hitters he faced.
"He settled in," Royals manager Ned Yost said of Guthrie. "He started executing his pitches to a high degree. I mean, really started spotting his pitches well, really used the inside part of the plate effectively."