ST. PETERSBURG, Fla. — The Tampa Bay Rays are a great organization. They really are. You’d rather be them right now than the Red Sox.

But they are stubborn.

They live and die with their pitching.

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And they have been successful because they have not succumbed to trading off starting pitching to improve their offense with the exception of dealing Matt Garza to the Cubs because he was on the verge of costing too much money.

They stick to their beliefs. They will rely on pitching depth and in the end they dare you to beat it. Right now, it appears the Rays won’t be able to pitch their way to the playoffs.

After bowing to the Red Sox, 5-2, Monday night, the Rays are falling farther and farther back of the final wild-card spot (they are five games behind No. 2 Baltimore, and 5½ back of the Yankees in the divisional race).

Will that change their approach this offseason? Will they finally sacrifice pitching to get some much-needed offense? Will they improve their defense, which is ranked the worst in the American League?

In the past, the answer — at least to the sacrifice of pitching — has been no.

The Rays have a 3.22 team ERA, best in the majors, and a 2.62 ERA since the All-Star break, also best in the majors. They were first with an opponents’ average of .231 and 1,225 strikeouts. The last team to lead in all three categories was the 1999 Red Sox.

The last five teams that finished with an ERA as low as the Rays’ went to the World Series.

But their offense tells a completely different story. They have scored 21 runs in their last seven games. They’re hitting .237 as a team, 27th in the majors.

Last offseason, they brought back Carlos Pena and signed Luke Scott, hitting .194 and .218, respectively. With limited resources, they know they can’t make mistakes and it looks as if they made two of them.

They never really addressed their catching, signing Jose Molina, who has taken on way too much of the chores. His game has declined steadily according to scouts who watch him regularly, and he’s hitting only .201.

They have a terrific all-around player in Ben Zobrist. Their superstar is Evan Longoria, who couldn’t play last night because of sore legs. They have gotten a lot out of Jeff Keppinger .(.317), and B.J. Upton continues to be an underperforming athlete. Upton, who has hit 13 of his 23 homers in the last 35 games, will be a free agent after the season and it’s unlikely the Rays will be able to retain him.

Part of the problem in dealing with their issues on offense is this number: 11,722. That was the attendance at Tropicana Field Monday night. The revenue stream simply isn’t flowing. The Rays are last in attendance, so they have problems stretching the payroll beyond $60 million even though they get a nice haul of revenue sharing from the big-market teams.

A new stadium isn’t anywhere in sight, so they develop pitching, keep it, and then lose it if the player becomes too expensive. The Rays have a $9 million option on James Shields and it appears they will pick it up, but they likely won’t re-sign Upton, who could seek a five-year deal at about $70 million. Yes, some team (Washington? Boston?) will give him that.

There’s no doubt that the Rays, who have lost six of their last seven, have been dying slowly the past week. They are beaten down by the fact that they can’t score runs. They are beaten down by their shoddy defense and poor hitting.

“This has been ongoing, this has been a seasonal adventure or misadventure, so it’s not like we’re all of a sudden not hitting, which would indicate you’re feeling pressure and not hitting,” Rays manager Joe Maddon said. “We have not been hitting pretty much all season. Look at our all-around rankings. They are not good. We have been able to remain solvent because our pitching has been so good. At this particular juncture we have to conjure up runs. That starts with better at-bats, accepting your walks, using the whole field, attacking the ball harder. That’s when defenders miss it.”

The frustration of the season spilled into the dugout Monday night when starting pitcher Alex Cobb, who had no-hit the Red Sox for five innings, was touched up for a pair of runs on Jacoby Ellsbury’s homer in the sixth.

Cobb and Molina got into a shouting match in the dugout and they had to be separated by teammates.

Maddon said the argument was not over Molina botching so many balls.

When pressed about whether he was upset about the players having to be separated, Maddon said, “I’m not unhappy. Garza and [catcher Dioner] Navarro had a nice spat in Texas [in 2008]. That’s overblown. That can be a good thing. It’s fine right now. It’s very fine.”

“We discussed everything. It’s all good. You have it in your household. You’ve yelled at the kids, haven’t you? Your kids do something naughty, you straighten it out and everything’s fine. In the dugout, we did it in real time,” Maddon said.

The lowly Red Sox are now 8-5 against the Rays this season. These are games you should win if you’re trying to contend. And a very quiet Rays clubhouse knew it.

“That’s a dumb question,” responded Upton to an inquiry about whether the Rays were pressing. “No, we’re not pressing.”

Asked if they could come out of their offensive doldrums, Upton said, “We’re going to have to if we want things to go the way we expect it. We have to find a way to bounce out of it. We have to find a way to do it.”

The Rays depended on Boston’s horrible collapse last season to sneak into the playoffs. The only way that can happen now is if the Yankees, Orioles, or A’s collapse over the last 15 games and the Rays rebound.

Crazier things have happened and the Rays never rule themselves out because their pitching is simply too good.

But the name of the game is scoring runs. And for the longest time the Rays haven’t been able to solve the problem.