CLEVELAND – The Twins packed up and headed to the airport in a hurry on Thursday. They didn't need to watch the Guardians celebrate something that is rapidly slipping away from the Twins: a playoff berth.

Andrés Giménez lined a Caleb Thielbar fastball into right field for a single, scoring courtesy runner José Ramírez from second base, and the Guardians formed a giant, jubilant scrum in Progressive Field's infield, hugging each other after their 3-2,10-inning victory clinched a spot in the postseason for the sixth time in nine years.

The Twins, meanwhile, fell into a tie with the idle Tigers for the final American League wild-card berth with nine games remaining, though the Twins do own the tiebreaker via their 7-6 record against Detroit this season. The loss also officially made the Twins the former AL Central champs, their hopes of back-to-back titles now mathematically impossible.

"It can be hard. It can be excruciating at times," Twins manager Rocco Baldelli said after the Twins' 11th loss in their past 16 games. "You could make a pretty reasonable statement that we were in a spot to win all four games here. You want that. We've got four chances to win games, and we walk out with one. That's not going to be satisfying, there's no way around that."

Especially the way this one played out: The Twins took a 2-1 lead on Manuel Margot's fifth-inning double — but didn't get another hit in the final 5⅔ innings against the Guardians' bullpen, a unit that Baldelli called "the best bullpen in the history of baseball, by a lot of measures."

That bullpen gave up only nine hits and four runs in 19⅓ combined innings in the series. The Twins scored precisely as many runs, 13, as the Guardians did in the four-game series, but it sure didn't feel like it, did it?

That's been the story of the entire season between these teams: Cleveland dominated the season series 10-3, even though 12 of those games were decided by three runs or fewer.

"They showed why they're the better team, why they've been better this year," said catcher Ryan Jeffers. "They're able to finish those games out, the games we haven't been able to, from both sides. Not just the pitching side, but from adding the extra run when they needed it."

The Twins still had plenty of opportunities in this series, and even in the finale, though they collected only three hits. Margot's fifth-inning line drive to left-center brought home Kyle Farmer, who had doubled, and when center fielder Lane Thomas briefly allowed the ball to get away from him, Willi Castro, who had walked, scored from first base.

But that was it for offense by the Twins, who scored only 38 runs, or 2.9 per game, against Cleveland this year.

Even in the 10th, an inning in which they started with a free runner on second base and loaded the bases with a hit batter and a walk, the Twins couldn't come up with a hit from their most feared hitters, Carlos Correa and Byron Buxton.

"We have Carlos and Buck coming to the plate. It's a great opportunity to win the game. I want to be in that spot," Baldelli said. "What else do we want in the 10th inning than to have those guys at the plate with the bases loaded? … When we have those opportunities, we have to come though."

Correa, though, popped up next to the Twins' bullpen for the second out, and Buxton ended the inning with a soft fly ball to right.

The Guardians, meanwhile, put runners on base in each of the first eight innings, including three consecutive softly hit singles against lefthanded reliever Cole Irvin in the sixth inning. Those hits loaded the bases, and shortstop Brayan Rocchio lifted a medium-depth fly ball to drive home the tying run.

Simeon Woods Richardson contributed a relatively effective start, despite allowing baserunners in each of the five innings he pitched in. He walked only one batter and struck out six, his highest total in a month.

But Kyle Manzardo belted a changeup into the right-field seats in the first inning, then whistled a single into right field in the third, the two hardest-hit balls Woods Richardson gave up.

So when the Guardians' designated hitter came to the plate again with a runner on base and two outs in the fifth, Baldelli took no chances, removing Woods Richardson despite the Twins' 2-1 lead at the time. It was Woods Richardson's 17th no-decision start of the season, more than any other starter in the majors.

Despite the painful series, Baldelli said he still believes the Twins have big things to achieve this year.

"We're still sitting here in a spot where we have an opportunity to go to the playoffs and win. It doesn't feel like that when you lose three out of four, when you're not playing your best," the manager said. "We have great players. We just have to go out there and keep playing hard. … I believe in our guys."