CLEVELAND -- The Yankees never expected this to be simple, and their American League Division Series-opening showdown with Trevor Bauer on Thursday didn't do anything to change that. Yet as a team that most expected would be on the outside looking in this postseason, they would love to prove a

CLEVELAND -- The Yankees never expected this to be simple, and their American League Division Series-opening showdown with Trevor Bauer on Thursday didn't do anything to change that. Yet as a team that most expected would be on the outside looking in this postseason, they would love to prove a few more people wrong over the next few nights.

"They need to beat us three times," Dellin Betances said after the Yankees' 4-0 loss to the Indians in Game 1 of the ALDS presented by Doosan at Progressive Field. "They've got great pitching, but at the same time, we believe in the guys we have here. We've always fought back when we're down. Tomorrow we'll try to split the series."

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Having turned in a sharp eighth-inning outing in which he struck out the side, Betances said that he felt the best that he has in a while. That provided a glimmer of forward-looking optimism on a night when the Yankees were limited to just three hits -- two off the bat of second baseman Starlin Castro .

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"Every playoff game is really big, but obviously when you're down 0-1, you'd like to get even and go home with it," Chase Headley said. "It's the playoffs. Everybody is good. This is a really good team, and we know it's going to be a challenge. Nobody said it was going to be easy."

Bauer made Tribe manager Terry Francona seem prescient for holding back ace Corey Kluber until Game 2, as the right-hander carried a no-hitter through 5 1/3 innings before Aaron Hicks broke up the bid with a double off the left-field wall.

The Yanks recognize that they figure to have their work cut out for themselves with Kluber, an AL Cy Young Award front-runner who limited New York to three runs and six hits over 17 innings (1.59 ERA) in two starts this season, striking out 18 against two walks.

"In a series, you're going to have to face him, whether it's [Game] 1, 2 or 3," Brett Gardner said. "We've got to play well against him. We've got to pitch well against them. They've obviously got a good team. We'll come out and have a good approach against him and find a way to score a couple runs."

There is confidence on the Yankees' part in sending Carsten Sabathia to the mound as a stopper; the big left-hander was 9-0 with a 1.71 ERA in 10 starts following a Yanks loss this season.

"That's something I don't even think about," Sabathia said. "You just go out and try to perform well. It's just one of those things where it's one of those stats this year, I guess."

Should the Yankees scrape a few runs together off Kluber -- Headley and Gary Sanchez have both homered off him this season -- Yanks manager Joe Girardi figures to have the benefit of a rested bullpen, thanks in large part to Jaime Garcia , who hurled 2 2/3 scoreless innings in Game 1.

That permitted Girardi to stay away from closer Albertin Chapman , Chad Green , Tommy Kahnle and Player Page for David Robertson after the quartet was called upon to record 26 outs Tuesday night in the AL Wild Card Game against the Twins.

"I think Jaime did a tremendous job keeping them where they were, and obviously Dellin came in, and [Adam] Warren did a good job, too," Headley said. "We'll have some fresh arms tomorrow. They're the least of my worries. They do a pretty good job for us."

With Betances having regained the feel for his breaking ball by throwing at a bucket repeatedly during Wednesday's workout, the Yankees' bullpen may offer a legitimate challenge to Cleveland's relief corps for the rest of the series.

"You can't tell anybody in that room we're underdogs," Sabathia said. "We feel like we should be here, and we feel like we can play with anybody."

Bryan Hoch has covered the Yankees for MLB.com since 2007. Follow him on Twitter @bryanhoch and on Facebook.