The loss marked the first time the Cardinals have dropped back-to-back games since they lost three in a row from April 27-29.
"We are playing good baseball," Kelly said. "But it is baseball. You're going to lose some games, you're going to win some games. I mean, two in a row is not that big of a deal. We'll be fine. We'll get right back out there tomorrow."
In his first start of the season, Kelly pitched a solid 5 2/3 innings through steady rain, allowing two runs (one earned) on four hits and one walk.
Before Wednesday, Kelly had thrown more than 27 pitches just once this season, when he tossed 62 in three innings of relief against the Dodgers on May 25. But Kelly threw 80 pitches in the loss.
"I was happy with that," Kelly said. "Especially since [in] yesterday's game, our bullpen did such a great job in that many innings. I knew, I was like, 'Oh man, got to go as many pitches as my arm can go and we'll see what happens.'"
Manager Mike Matheny said he expects to give Kelly at least three days of rest before working him back into the bullpen.
Rookie Shelby Miller was originally slated to pitch Wednesday, but his last start was rained out and was rescheduled as part of a doubleheader Saturday, which knocked the rotation out of sync.
"Joe did a good job for us," Matheny said. "We needed that. He was good. He had a good sinker working. Probably the best changeup we've ever seen him throw. A little trouble getting his breaking balls going, but overall just a really big outing for us."
Kelly's lone hiccup came in the second inning when he gave up a double to Martin Prado and allowed Didi Gregorius to drive him in with an RBI single. Kelly left one runner on for Randy Choate in the sixth, but Willie Bloomquist scored on a fielding error from Matt Holliday on Jason Kubel's deep fly ball, spoiling Holliday's perfect fielding percentage this season. Running back toward the left corner, it appeared Holliday had the ball in his glove but lost control of it.
"Any time they're going back, it's a tough play," Matheny said. "I thought that was one he had and just couldn't hold on to it."
Choate gave up a double, an RBI single and hit one batter, but he secured two outs before turning the ball over to Cleto. The right-hander hit Bloomquist with a pitch to load the bases, then Goldschmidt cleared them with his 421-foot blast.
"He thought that was a good pitch; it was down," said Jaime Garcia, talking on behalf of Cleto. "He's just a good hitter and he made a pretty good swing on the ball."
Despite his struggles, Cleto was forced to stick out the final two innings since limited options were available in relief. With the bullpen exhausted, the Cardinals needed someone to eat up the innings when the game was out of reach, and Cleto did just that.
"You just hate to see somebody get hit around like that," Matheny said. "We would have loved to have got him out, but we just didn't have the ability to do that, to help him get out of it. We needed somebody to come in and throw innings for us, and that was the purpose of getting Maikel here."
In the eighth, Cleto struck out one batter and retired another, but he loaded the bases again with a hit by pitch, a line-drive single and a walk. Back-to-back singles from Gerardo Parra and Bloomquist drove home three runners before Cleto could strike out Goldschmidt for the third out. He settled in to strike out two batters in a scoreless ninth.
The Cardinals couldn't keep pace with the D-backs throughout, managing just one run in the fourth and another two in the seventh. Carlos Beltran drove in the two runs with a hard single down the left-field line, but he was thrown out at second trying to stretch it to a double. Arizona starter Wade Miley allowed all three St. Louis runs on 11 hits and one walk.
The Cardinals outhit the D-backs 12-11, but couldn't capitalize, stranding eight runners on base.
Both Matt Carpenter and David Freese kept their respective hit streaks alive. Freese, one game ahead of Carpenter at 15 straight games, went 1-for-4. Carpenter, per usual, was excellent in the leadoff spot. One night after getting plunked by three pitches, Carpenter went 4-for-5, bringing his team-leading multhit games total to 24.
"When you see a guy get hit three times, he wants to come out the next day and show them something," Matheny said. "And I think he did that. Got right back into his game plan. ... He's not varying from what he knows works for him, and it's working."