– Brian Dozier agrees that the Twins could have done more, won more, to persuade the front office to keep adding to the roster.

They have not had more than a four-game winning streak this season, so they have been unable to get on a run that would have certified their playoff worthiness.

Still, when Dozier awoke to the news on Sunday that the Twins had traded lefthander Jaime Garcia to the Yankees for two pitching prospects — only six days after acquiring him from Atlanta, and a day before the nonwaiver trade deadline — it was as if hot coffee were poured in his lap.

“That’s frustrating within itself, to not go on a little run,” Dozier said. “A couple of games could have gone differently. We should be adding [players]. It’s frustrating.

“I know all these guys feel the same way.”

The reality is that the Twins are seven games behind Cleveland in the American League Central and five behind Kansas City for the last AL wild-card spot.

Their position prompted Chief Baseball Officer Derek Falvey and General Manager Thad Levine to switch gears. So Garcia was traded for pitching prospects Zack Littell and Dietrich Enns. The Twins sent the Yankees a little over $4 million in the Garcia deal, allowing New York to pay Garcia the minimum the rest of the season.

Garcia won his only start for the Twins, giving up three runs in 6 ⅔ innings on Friday at Oakland. He is expected to make his Yankees debut on Thursday at Cleveland.

Littell, 21, is 14-1 with a 1.87 ERA this season between Class A Tampa of the Florida State League and Class AA Trenton of the Eastern League. At Trenton, he’s 5-0 with a 2.05 ERA. In 44 innings, he has walked eight and struck out 52. An 11th-round pick of the Mariners in 2013, Littell was dealt to the Yankees last November for lefty reliever James Pazos.

His fastball sits in the low 90s, but he also has command of his curveball. He will be assigned to Class AA Chattanooga.

Enns, 26, was a 19th-round pick out of Central Michigan in 2012. He is 2-1 with a 1.99 ERA this season, mostly with Class AAA Scranton-Wilkes Barre. One scouting report has him touching the low 90s, with a good changeup and decent slider/curve. He’s headed to Class AAA Rochester.

Falvey and Levine have until 3 p.m. Monday to make any more trades without waivers. The Boston Red Sox have checked on the availability of closer Brandon Kintzler, who is a free agent at the end of the season, and Dozier and Ervin Santana are valued pieces.

“I’m a little more at ease this time,” said Kintzler, who was nearly traded last year before the deadline. “Last time, I was pretty stressed out about it. I had never been a part of it, and I really wanted to stay. I really liked where I was at. I know that, right now, with my situation, it’s a business and it is what it is.

“I would love to stay and finish what I started. If not, there’s always a chance to come back.”

Kintzler said teams 10 games out of first place at this time of the year have stormed back. Why not the Twins?

“This is the same group that was in first place for two months,” he said. “We easily could be 4-1 on this road trip. We have to get back to grinding together to win some ballgames.”

Kintzler said that before the Twins blew another lead Sunday.

Garcia was in Atlanta when the trade was announced, collecting some belongings to bring to the Twin Cities. Those belongings are now headed to New York. Twins manager Paul Molitor spoke with Garcia by phone Sunday morning, but most teammates never had a chance to wish him well.

Molitor told his team before Sunday’s game that expectations don’t change, even if the front office decides to sell.

“Get over it,” he said. “That’s the way it works. We are where we are. We’re one good run away from this having a different look. The last 10 days went against us. We’re still playing a lot of teams we need to pursue down the road.”