But even though they're finished for 2013, this franchise is establishing a legacy that is the envy of many other Major League teams.
The way the Rays play the game, the manner in which they approach this greatest of all sports even though they are frequently out-manned, and out-spent, is a tribute to their impressive philosophy.
That was certainly on display in this series, even though it ended on a distasteful note.
The Red Sox, after falling to the gutsy Rays, 5-4, on Monday night, seized the moment with a 3-1 come-from-behind victory at Tropicana Field in a game that began on Tuesday and stretched into the wee hours of Wednesday.
The multi-talented Red Sox are now headed to the AL Championship Series against either Detroit or Oakland, but they'll need a breather after having their hands full with Tampa Bay.
After being no match for Boston in the first two games of this best-of-five tournament, the Rays came to life and showed the heart and determination that has become their trademark since they turned losing into winning in 2008.
Before a packed house at The Trop, manager Joe Maddon pulled out all the stops in Game 4 and after six innings his troops were walking a 1-0 tight rope.
The Red Sox, however, rallied for two runs in their seventh, using the blazing speed of Jacoby Ellsbury and Shane Victorino, plus a wild pitch, to take a 2-1 lead. They padded their lead with a run off Fernando Rodney in the ninth.
Yes, they were outplayed by the powerful Red Sox. After losing the first two games in Boston and looking like they didn't belong on the same field, that they could come back, win Monday night and come close to forcing a fifth game is amazing.
That is what Tampa Bay Rays baseball is all about.
The Rays, as they did in the ALDS, could look like champions one moment and just the opposite in the next game.
Inconsistency plagued them all season.
"With 90-plus wins [actually 92], it's been a pretty good year regardless of what anyone else might want to think," said Maddon, who used a record nine pitchers on Tuesday night and had David Price warming up for a possible 10th inning. "You're always going to talk about the different levels of success.
"And what is ultimate success is probably winning the World Series. But I also think there are different levels of success. And maybe more important things like making sure that your children, when they grow up are happy. There's a different way to look at the whole thing.
"I'm really proud of our group. We had some really good moments and some really bad moments, but at the end of the day, you still win 92 games and that's pretty good."
Maddon added: "I don't want to use a cliché, but there's nothing to hang our heads about. There really isn't."
The Rays were created by expansion in 1998 and until 2008 were perennial losers. On two occasions, they lost over 100 games. But in '08, they turned the corner, won the American League pennant and went to the World Series, losing to the Phillies.
They've been to the postseason four of the last six seasons.
And with that, they're building their legacy.
"There have been really cool memories for us here in this organization," Maddon said. "And like I said in a brief period of time. We're building our tradition right now.
"The tradition has to begin somewhere. We're living it, so we don't have the benefit of 50 years from now looking back. All these games matter, when you start building a tradition, all this stuff, allure counts."
Boston skipper John Farrell, a cinch to win AL Manager of the Year, put it this way: "I'm assuming our next opponent is going to be as tall a challenge as Tampa Bay is. They pitch extremely well. They play a complete game. They're athletic and they play very good defense."
In the end, the Red Sox were the superior team, maybe the best in the AL, if not the Major Leagues. Time will tell.
The Rays just were not able to stand up to the Boston pitching.
In the Tuesday/Wednesday loss, the heart of the Rays' batting order -- James Loney, Longoria, Ben Zobrist and Desmond Jennings were 0-for-14, with five strikeouts. Loney hit into a fourth-inning double play.
Consider this: The Rays went 5-for-28 with runners in scoring position, a .179 average. During the regular season vs. Boston they hit even worse -- .153 with runners in scoring position.
But as Farrell said: "You never feel like you're comfortable going up against Tampa Bay."
That is the tradition the Rays are building and years from now it will be the center piece of their legacy.
Hal Bodley is the senior correspondent for MLB.com.