ST. LOUIS — The Nationals can’t say exactly how much of the $126 million they gave Jayson Werth was for his experience, intangibles and ability to set the tone of a major league clubhouse. But it was a big chunk because he’s played in five times as many postseason games as any other Nat. From the day Werth arrived last season, General Manager Mike Rizzo said that attitude, since rebranded “Natitude,” was as big a part of the outfielder’s total value as any one physical gift.

So, it’s no accident Werth’s locker was the first one by the door as you entered the Nats’ silent clubhouse after a homely 10-4 loss to the Cardinals on Sunday that kept Washington’s magic number at one to win the NL East.

Frustration hung in the air. “I had the first chance to clinch it,” Ross Detwiler said of the first first-place finish in generations. “I sucked,” he said after allowing seven runs while getting only seven outs on 81 ugly pitches.

Nearby, a Cards attendant tried to hand Manager Davey Johnson a postgame box score.

“I don’t read that crap. I live it,” Johnson said tartly. “I don’t read it when we win and I’m damn sure not reading it after that one.”

Werth, who usually wears defeats as hard as anyone in the Nats’ room, had a different viewpoint after a series here that also included a 12-2 beatdown Friday in which Edwin Jackson, a crucial postseason starter, was demolished for nine runs while getting just four outs.

“We played all season to get in position to win one game and now we get to do it in front of our own fans,” Werth said. “Can’t wait.”

Those last two words are the ones that count. You can’t put a price on them because they come from Werth’s own experience with the powerhouse Phillies, not out of any leadership manual. Werth knows how hard it is to clinch your first NL East title. There’s no place for frustration or embarrassment in the equation. There’s only room for “can’t wait.”

Five years ago, the Phils entered the next-to-last game of the season with a one-game lead and, as if by some great gift of the scheduling gods, got to play one of the least talented teams ever to wear big league uniforms — the pesky ’07 Nats, who in the preseason were predicted to lose 130 games.

The Phillies lost that day to the Nats and humble little lefty Matt Chico to fall back into a first-place tie on the last day of the season. That’s anguish. That’s egg on your face. That’s “what’ll they say in Philly if we blow this.”

Now the tables are turned as the Phils come to Washington for the last three games of the season, starting Monday night. So far, the Nats face only a fraction of the uncertainty and pressure that is the rule in pennant races.

For the Nats not to win the division title, a seven-way parlay would have to hit for the Braves, which is more than a 100-to-1 shot. The Nats would have to go 0-3; the Braves would have to go 3-0 and then beat Washington in a one-game playoff on Thursday at Nationals Park.

The arithmetic powerfully favors a celebration on South Capital Street soon. But this is unequivocally a case of the sooner, the better.