Mike Mussina fields the ball in the fourth inning of Tuesday's 3-1 Yankees win. (Frank Gunn/Canadian Press)

The New York Yankees won the battle but lost the war — beating the Toronto Blue Jays 3-1 on Tuesday night, only to be bounced from playoff contention anyway.

Jason Giambi homered and scored twice in support of Mike Mussina, who pitched five masterful innings for the Yankees (86-71).

"I thought we would be playing Oct. 1, I really did," Yankees manager Joe Girardi said. "That is hard to swallow because you look forward to that baseball in the crisp air."

New York had not missed the playoffs since 1995, but the Boston Red Sox clinched at least the American League wild card with a 5-4 victory over the Cleveland Indians on Tuesday — and eliminated the Yankees in the process.

"It is really devastating," Yankees third baseman Alex Rodriguez said. "It makes you sick to your stomach.

"One thing is to lose in the post-season, one thing is to be eliminated. That is an experience we don't want to have again."

The Yankees reached the playoffs in 12 straight seasons, but the Atlanta Braves hold the major-league record of 14 in a row.

"It basically boils down to we were not good enough," said Yankees captain Derek Jeter, who failed to reach the post-season for the first time in his career.

"That is the only way you can put it. Our team did not play well enough the whole season in order to get to where we needed to be.

"It is a huge disappointment. That is pretty much all you can say."

Added Mussina: "We have been disappointed for a little longer than just today. It has been a tough summer for us."

Mussina (19-9) scattered four hits over five scoreless innings, striking out six batters without issuing a walk.

He also shook off a line drive from rookie Travis Snider that struck him on the right elbow in the third inning.

"I said 'I'm all right,' and that was good enough for them," Mussina said. "Right now, it is stiff when I try to bend it."

Mariano Rivera recorded the final three outs for his 38th save in 39 opportunities this season.

Litsch suffers loss

Jesse Litsch lasted seven innings, yielding three runs on five hits and one walk in a losing cause for the Blue Jays (83-74).

Litsch (12-9) posted a career-high eight strikeouts.

New York opened the scoring in the top of the second inning when Giambi singled, advanced to third base on Xavier Nady's double and scored on Robinson Cano's RBI groundout.

Giambi put the Yankees ahead 2-0 in the fourth inning with a solo home run to right-centre field, his 32nd of the season.

In the seventh, Cano doubled, moved to third on a wild pitch and scored on a passed ball credited to catcher Gregg Zaun.

Toronto trimmed it to 3-1 in the bottom of the seventh inning on Scott Rolen's RBI single, but left the bases loaded in the eighth when Yankees reliever Joba Chamberlain whiffed Lyle Overbay on a called third strike.

With files from the Canadian Press