New York Yankees' Alex Rodriguez reacts after striking out with the bases loaded against the Detroit Tigers during the seventh inning of Game 5 of their MLB American League Division Series baseball playoffs at Yankee Stadium in New York
New York Yankees' Alex Rodriguez reacts after striking out with the bases loaded against the Detroit Tigers during the seventh inning of Game 5 of their MLB American League Division Series baseball playoffs at Yankee Stadium in New York, October 6, 2011. Reuters

The New York Yankees' annual mission statement is to win the World Series so anything short of that is a disappointment. Losing a deciding playoffs game at home makes defeat all the more stinging.

After extending the best-of-five division series with a 10-1 Game Four romp in Detroit on Tuesday, the Bronx Bombers fell 3-2 to the Tigers at Yankee Stadium on Thursday and were eliminated from the playoffs.

We felt coming into this game after Game Four that this was a game we needed to have at home, but we came up short, said Yankees third baseman Alex Rodriguez, Major League Baseball's highest-paid player at $31 million this season.

This was a game we felt really good about. We should have won. We had opportunities there late and a big hit there and maybe things are much different. This one hurts.

Rodriguez was one of the primary culprits in a succession of missed chances for the Yankees, who twice loaded the bases with one out and managed only a single run from the twin threats while stranding 11 baserunners over the course of the game.

A-Rod, who struck out three times, whiffed with the bases full with one out in the seventh against reliever Joaquin Benoit, and struck out against closer Jose Valverde to end a contest that sent Detroit to the American League Championship Series against the Texas Rangers.

When you have opportunities like that you got to keep the momentum going, Rodriguez told reporters crowded around his locker. A sac fly, a base on balls. I didn't get the job done.

That was a dream at-bat. Those are at-bats that I relish. I had a lot of confidence I would get something done there in a positive way ... You pay to be in those situations.

Yankee first baseman Mark Teixeira produced the one score from those bases-loaded threats by drawing a walk to force home a run in the seventh that made it 3-2.

Give them credit, Teixeira said. They pitched really well. We just could've been a little better. One hit better. One more hit tonight, and all series long. If we could've been a little better, we win the series.

The Yankees won their two games 9-3 and 10-1.

Detroit claimed the close ones, however, winning 5-3, 5-4 and Thursday's clinching 3-2 victory.

Losing is tough, period. But losing at home is even tougher, said 40-year-old Jorge Posada, the former catcher who might have played his last game as a Yankee after winning five World Series rings in pinstripes.

They made the right pitch at the right time ... they made great adjustments throughout the whole game.