Moore, who tossed 62 strikes in the 105-pitch outing, was displeased with the lack of a fastball command early in the count against the A's.
"The biggest thing is getting ahead and staying ahead," said Moore, who issued three walks while striking out four. "I have to have better fastball command, especially early, if I want to accomplish things on the mound.
"It's not necessarily about being too fine with the corners on the pitch. It's more about being comfortable throwing it early in the count."
The Rays lost two straight for the first time since enduring a four-game losing streak a week into the regular season.
"We pitch our normal game there, we win," Maddon said. "[Moore] looked good right out of the shoot, but he just lost the strike zone. He's going through that youthful transition. It's going to happen. It happened with all of our young pitchers. David [Price] went through it."
The Rays lost for just the second time when scoring at least five runs over their last 43 games, a stretch that began on July 28, 2011 against the A's in Oakland. The only other loss was a 13-5 defeat to the Red Sox on April 14 in Boston.
"Normally, when we score five runs, we get the 'W,'" Maddon said. "It just wasn't our day."
With 10,000 kids of the 23,873 in attendance at Tropicana Field sporting Joe Maddon replica sunglasses, the Rays heated up in the first inning by scoring four runs off A's left-handed starter Tommy Milone, highlighted by an RBI-single by Sean Rodriguez and a two-run single by Matt Joyce.
After going 1-for-13 over the four games, Joyce got back on track with a 3-for-4 performance, including two hits against Milone and one against lefty reliever Brian Fuentes.
"I just am feeling more comfortable against lefties the more at-bats I get against them," said Joyce, who was just 4-for-23 against left-handers before Sunday. "The key is to let the ball travel deeper into the zone, not pulling off the ball and striding through it longer."
This was the second time in his career that Joyce has notched three hits against left-handers in one game. the previous game came last August 28th against the Blue Jays.
During the four-run first inning, the Rays may have lost another player when Desmond Jennings injured himself sliding headfirst into home on a sacrifice fly by Jeff Keppinger. Jennings left the game after making the second out of the second inning when he was thrown out at first on a grounder to short.
"He's still being evaluated and we will know more tomorrow," Maddon said.
Elliot Johnson moved to left field to replace Jennings at the beginning of the third inning and Will Rhymes entered the game to play second for Johnson.
Moore surrendered five runs in the third and three more in the fifth, while Milone followed up the first inning by retiring nine of the next 11 batters he faced before giving up a solo homer to B.J. Upton in the fifth inning.
Milone left after tossing 94 pitches, 57 strikes, over five innings. He allowed five runs on five hits while striking out one and walking four.
"Their pitcher recovered nicely," Maddon said. "Another thing is, their defense wasn't supposed to be good and they played great defense against us. They played well and their pitcher pitched great."
Moore's third inning saw Yoenis Cespedes and former Ray Jonny Gomes collect RBI singles before Brandon Inge crushed an offering from Moore deep into the left-field seats for a three-run homer. In the fifth, Gomes had an RBI double and Daric Barton plated two runs with a double.
"The biggest problem they had was they're weren't hitting and they hit the ball well," Maddon said.
The A's scored more than seven runs in a game for the first time since last Sept. 10 against the Rangers, snapping a franchise-long streak of 45 games with six runs or less. Oakland has won four of their past five games after losing three in a row.
"When you get down by four runs right away like we did, you're hoping it doesn't snowball," Inge said. "It could have turned into a 10-0 game. We needed to get something quick."
On Inge's at-bat, Moore had second base open with two outs, but elected to go after the 10-year veteran with a 3-1 fastball.
"Right there, Inge had him backed in a corner, and had a lefty on deck," Maddon said. "That's a youthful mistake right there."
After Moore exited the game, Burke Badenhop tossed 1 1/3 scoreless innings before giving way to Wade Davis, who made his first appearance since an outing against the Mariners on May 2. Davis allowed a run and three hits with two strikeouts and two walks over two innings.
Cesar Ramos, who was recalled from Triple-A Durham earlier in the day, finished the game with a perfect ninth.
"He threw the ball well," Maddon said. "The biggest problem we've had with him is him not being able to throw strikes and he did so effectively today."