MINNEAPOLIS -- Shortly after taking the ball from Joey Estes with a runner on, one out and only 75 pitches in the sixth inning, manager Mark Kotsay pulled the rookie aside in the A’s dugout for a discussion.

“I told him, ‘Your future is bright,’” Kotsay said. “You’re going to get the ball in those moments to go through that inning in the future.’”

If Estes -- Oakland’s No. 13 prospect, per MLB Pipeline -- develops as the organization expects him to, he will one day get a chance to work out of such a situation. That day was not Wednesday, in what was just the 21-year-old’s second Major League start over the final week of a rebuilding season for the A’s.

Estes walked off the mound at Target Field with a two-run lead in line for his first big league win. Several minutes later, though, that possibility evaporated. Kyle Muller came on in relief and surrendered a game-tying homer, and the A’s ultimately fell to the Twins, 6-4.

With Wednesday marking his final start of 2023, Estes will have to wait until next year for that first win. Nonetheless, the outing was a solid showing to close out his first season in the Majors.

After a nerve-wracking debut last week at the Coliseum, in which Estes “couldn’t feel” his legs for about two innings, in start No. 2 he looked a lot more like the pitcher who earned himself a call to Oakland after beginning the season at Double-A Midland. Across 5 1/3 innings, Estes limited a playoff-bound Twins squad to three runs on six hits with one walk and five strikeouts.

“This is a kid that isn’t going to beat himself,” Kotsay said. “He’s going to attack hitters. Overall, his night was great. He got into that sixth inning with a lead. … This kid is a competitor. You can see the way he is out on the mound. He’s got a presence about him."

Brushing off a leadoff homer by Edouard Julien on the first pitch he threw, Estes worked with runners on in each of his innings and managed to limit the damage. His best inning was a shutdown fifth, in which he induced a double play on Julien before striking out Jorge Polanco on a slider.

Of Estes’ 75 pitches against Minnesota, 53 were strikes. He recorded a total of 13 whiffs on the night, generating at least one swing and miss on all five of his offerings -- fastball, sweeper, slider, changeup and cutter.

“I was definitely way more comfortable out there than my first time,” Estes said. “Even in the first inning, I felt settled in. It was just a first-pitch ambush. Second inning was a little bit of a battle. But the whole game, I felt like I was pounding the zone and getting good results with that.”

Come next February, Estes will likely find himself in the mix with a group of talented young starters vying for A’s rotation spots. He will enter that battle having soaked in the experience of competing against a pair of playoff-contending clubs. His first start came against the Mariners, who remain entrenched in a tight American League West and Wild Card race.

“I’m just living in the moment,” Estes said. “Literally just taking advice from all these guys. Everybody knows what they’re doing up here. You’re always constantly learning every day. Being around these guys is helping to make me better.”

A struggling bullpen highlighted a loss that put the A’s at 110 defeats in a season for just the second time in franchise history and the first since 1916. After Muller gave up the lead, Dany Jímenez allowed the Twins to go ahead for good in the eighth.

For Muller, Oakland’s Opening Day starter, Kotsay described Wednesday’s outing as a “teaching moment.” With two outs in the sixth, the rookie left-hander reached an 0-2 count against Ryan Jeffers. In a situation that Kotsay said probably called for a fastball, Muller opted for a curveball that Jeffers sent well up the seats in left field for a game-tying homer.

“You’ve got a guy down 0-2 and he’s not caught up to the heater yet, and we throw a pitch not on the scouting report that is slow, and we get beat on it,” Kotsay said. “Those are those big moments that these kids without that experience go to, something that maybe they’ve done in the Minor Leagues, but you can’t get away with it here. … If we’re going to get beat, get beat on our best pitch. Tonight, that didn’t happen.”