The Yankees have won just three of their last 10 and averaged 2.5 runs during that stretch. It was more of the same on Sunday.
Shields struck out eight over six innings, allowing six hits and two walks. Seven of the eight baserunners Shields allowed wound up in scoring position, but the Yankees went 1-for-17 in those situations.
"It was a game of missed opportunities," shortstop Derek Jeter said.
"You give those guys credit, we've seen Shields for years now and he's as good as they come, especially with guys on base, he bears down. We got to find ways to score runs, especially when you have guys on third base and less than two outs."
New York's lone run came on an RBI groundout by Ichiro Suzuki in Shields' final inning.
Even with Shields out of the game the results remained the same.
Brett Gardner slugged a one-out triple in the seventh, but Royals reliever Aaron Crow stranded Gardner at third when Jeter (groundout) and Jacoby Ellsbury (strikeout) were retired.
Then in the ninth, Suzuki reached with a leadoff single and moved to second base on a wild pitch with none out. Suzuki eventually advanced to third, where Royals closer Greg Holland left him as Gardner struck out to end the game.
"We kept battling all the way up to the ninth inning, but that's not a bullpen you want to fall behind, they've got some guys in there that can bring it," Jeter said.
Yankees starter Hiroki Kuroda did his part, throwing seven solid innings. But a two-run second inning, highlighted by run-scoring hits from Lorenzo Cain and Mike Moustakas, was enough for the Royals.
"You get a great performance by Kuroda, and we didn't do anything with it," manager Joe Girardi said.
After a rough first two months (4.67 ERA in 11 starts), Kuroda has a 1.98 ERA in a pair of June outings.
"I thought he threw an excellent game, and it was back-to-back, which is a good sign for us because we know how important he's been to our rotation," Girardi said.
In the first two innings, the Yankees put five men aboard.
Gardner clubbed a leadoff single and Carlos Beltran later walked, but a Brian McCann flyout ended the threat.
The Yankees jammed Shields in the second by loading the bases with none out. But Shields walked away unharmed as he struck out Kelly Johnson and Jeter, and received a superb defensive play from first baseman Eric Hosmer in between.
"I pitched against them for about the 28th time [actually 29th] and they're always tough, so you've got to keep grinding," said Shields, who earned his seventh win. "I'm not going to give in. I'm not going to give them a cookie, especially there in the second inning with the bases-loaded."
An inning later, Ellsbury extended his hitting streak to 13 with a leadoff double. But New York wasted it as Beltran grounded out before McCann and Yangervis Solarte struck out to end the threat.
"A ton of opportunities. Bases loaded, nobody out, we couldn't score. Couple of times a runner on third, less than two outs, we're not able to score," Girardi said.
Kuroda opened the second inning with two quick outs.
But Salvador Perez preserved the inning by poking a single over second baseman Brian Roberts' head. Cain doubled him in, then Moustakas found a gap in left-center for an RBI single for a 2-0 Royals lead.
Over the next five innings, Kuroda allowed just one hit.
"I feel bad, Hiro did outstanding. He did exactly what you would want him to do," Jeter said.
Mark Teixeira did not start on Sunday -- Girardi gave him a routine day off -- but he pinch-hit against Holland in the ninth. Teixeira dribbled a grounder to second, moving Suzuki to third with one out.
The Yanks still have six games remaining on their road trip following Monday's series finale.
"You stay positive, you keep encouraging the guys, you put them in spots that you hope they can get it done, and you don't make too much out of one day. I mean, that's the only thing you can do," Girardi said.