The moment hit Moore and others when President Barack Obama read their names aloud to an overflowing room of fans and supporters.
"We don't get time to reflect very often in this game," Moore said. "But this is a moment to reflect on our accomplishments. This is special.
"Meeting the president is very special. It's a tremendous honor. Being able to share it with such a great group of people and their families, and to represent a very special city in Kansas City, is an honor."
The moment hit first baseman Eric Hosmer when he heard the "Let's go Royals" chant.
"When I heard that, it's like, 'We finally made it,'" Hosmer said. "It was cool to be a part of."
Most of last season's team was on hand, along with Moore, Glass, team president Dan Glass, senior vice president Kevin Uhlich, manager Ned Yost, Hall of Famer George Brett, Royals Hall of Famer Frank White and Kansas City mayor Sly James.
They stood as President Obama entered the room and instructed everyone to "Give it up for the World Series champions, the Kansas City Royals! I know many of you had been waiting a long time to hear this, so I'll say it again -- the World Series champion Kansas City Royals!"
Obama talked about the Royals' rise out of baseball's darkness and how their story was an inspiration to all.
"[Moore] coupled some of baseball's sharpest analytics minds with Ned's managerial style, which has produced a lot of wins," Obama said. "Not to mention his own Twitter hashtag -- #Yosted. All of which has combined to create one of the grittiest, most complete teams we've seen in a long time."
The speech certainly had its share of light moments, such as when President Obama read off the nicknames of some of Kansas City's stars, such as Alex "Gordo" Gordon, Mike "Moose" Moustakas, Salvador "Salvy" Perez and Eric "Hoz" Hosmer.
"These guys are all great players. Can I say, though, the nicknames aren't that creative," President Obama said to laughter from the team. "It's like, Barack 'Barack' Obama. You know? I mean, listen to this -- Hoz, Moose, Gordo. We're going to have to work on these."
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Hosmer said he'd get his teammates right on it.
"I guess we got to now if the president calls you out," Hosmer said. "We got some guys in the locker room who will figure it out."
President Obama also said he enjoyed the Royals' style of play.
"At the plate, you've got guys who hardly ever strike out," President Obama said. "They've been called, 'Basically the best contact team ever.' So fast, once [on] base, they're able to squeeze out extra runs, because as -- I love this quote -- as Jarrod Dyson puts it, 'That's what speed do.' ... That was a good quote. 'That's what speed do.'"
The ceremony was brief, perhaps 15 minutes, and some of the Royals chatted with reporters for a few minutes afterward before the team headed back to Kansas City.
Each member of the team will carry memories from the White House visit with them forever.
"To hear your name called by the president and to hear him run down the games we played in the postseason," Hosmer said, "you know he was watching. That's incredible."
Gordon, the longest-tenured Royals player, seemed especially moved.
"It took a while to get here, but we finally made it," Gordon said. "Me and Dayton kind of came up at the same time. We've had some struggles, but to be here in the White House and meet the president and hear the 'Let's go Royals' chants, it's something I'll never forget."
Perez did have one regret about the experience -- not being able to perform the "Salvy Splash" on the president.
"I wanted to," Perez said with a childish grin. "But people tell me, 'No, Salvy.' But what I really wanted was to take a selfie with the president, but the security guy didn't want me to."
It was a day that at least allowed the Royals to forget their 2016 struggles and simply enjoy the moment.
"What we accomplished is something we'll remember forever," Hosmer said.