BALTIMORE — On Tuesday afternoon, Red Sox general manager Theo Epstein said that hope had not been extinguished. While a glimpse of the standings revealed a daunting seven-game deficit to both the Yankees and Rays in the playoff chase, it was too early, he suggested, to surrender.

But how would the Sox identify the end of the season? Was there a certain number of games when hope would be gone?

“It’s kind of like the Supreme Court said about pornography,” said Epstein, citing a doctrine made famous by Justice Potter Stewart. ‘You’ll know it when you see it.' ”

The aftermath of Tuesday’s 5-2 loss to the Orioles looked very much like “it.”

The resolve that has characterized the Red Sox even in the face of the most painful losses was nowhere to be found. If hope had been chiseled away during the previous two defeats against Tampa Bay, Tuesday’s loss hit the fault line that led to its collapse.

In defeat, silence — both public and private — prevailed.

For what is believed to be the first time in his Red Sox tenure, Josh Beckett left the premises without making himself available to discuss an outing. Manager Terry Francona offered a few clipped observations of the defeat. David Ortiz addressed reporters only to say, “Not talking today.”

On a day that usually represents one of he highlights of the season (the team’s fantasy draft), players shuffled morosely toward their stations. The air remained dense with not just a loss, but with a sense of loss, on a night when the Sox fell eight games behind the Yankees in the division and remained seven behind the Rays in the wild card, failing to take advantage of Tampa Bay’s loss.

“I don’t think anyone here is not aware of what’s going on in the games with the other teams in our division. When one of those two lose and we can’t capitalize, you feel like you’ve kind of wasted a chance,” Mike Lowell said. “What can you do? We’re not playing with a lack of effort. Guys want to do well. It just seems like a play here or there doesn’t go our way.”

But at a time when the club requires something between what owner John Henry deemed a miracle and what GM Epstein described as a “super hot” streak, the Sox continued to lose ground while playing an Orioles club that has been a season-long thorn. The Sox are now 6-7 against the last-place O’s, a team against which the Yankees have gone 10-2 and the Rays 9-3. The Blue Jays, meanwhile, are a startling 12-0 against Baltimore. In other words, the Sox keep stumbling over the division doormat.

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The reality of the standings is this: The Red Sox are eight games out in the division and seven back in the wild card. In 2006, when the Sox admitted they were raising a white flag by trading David Wells on Aug. 31, Boston was eight games out in the division and 6½ back in the wild card.

Epstein insisted prior to the game that the 2010 club is in better shape than the 2006 vintage that represented the only season among the last seven in which the Sox did not reach the playoffs.

“[The 2006 season was] an example where our hopes for contention that season had completely dissipated based on the injuries and the talent we had left on the roster,” said Epstein, “whereas I think this club is capable of winning games.”

The problem is, even a “super hot” streak right now might not be enough. The 2007 Rockies, for instance, reeled off an incredible 14 wins in 15 games, but that amazing run only allowed Colorado to make up 4½ games in the standings.

Only three teams have ever erased seven-game deficits in the month of September (most recently, the 2007 Phillies, who wiped out that advantage against the Mets in the final three weeks). No team has ever overcome a larger hole in the standings in the season’s final month.

Those are the nearly impossible circumstances facing the Sox. For perhaps the first time, that harsh reality seemed to occupy the Sox clubhouse on Tuesday night.