What the Italians have faced off the field could easily have sapped them of their resolve. Their domestic league match-fixing scandal reached new heights Tuesday when a prosecutor urged the demotion of four Serie A teams for which many of Italy’s players star. Every Italian team member plays club ball at home — and 13 of the 23 play for the topflight teams under investigation.

While the Italians celebrated, the Germans collapsed in dismay.

“It’s bitter to lose like that,” Germany defender Philipp Lahm said. “We had set ourselves the target of reaching the semifinals, but once you’ve reached that, you want to go all the way.”

The home crowd lingered to cheer their heroes, singing and chanting their names and “Deutschland, Deutschland” after the match. Ballack and several others cried as they left the field after circling it to recognize their flag-waving fans. They were defeated, but unashamed.

“I already told my team in the dressing room that the team has every reason to be proud of themselves,” said Germany coach Juergen Klinsmann, who won the 1990 World Cup played in Italy. “They really achieved amazing things at this World Cup.”

They just couldn’t finish the heady Italians, whose technical mastery, particularly on defense, was surpassing.

The Azzurri heads to its first World Cup title game since losing to Brazil in 1994.

“These guys battled from the start and continued throughout,” Lippi said, referring as much to the scandal as the win. “It’s a great satisfaction. We look forward to next Sunday, whoever we play.”

Germany will play in the third-place game Saturday in Stuttgart, hardly where it planned to be.

“The boys are sitting there and have a bitter pill to swallow,” Klinsmann said. “It hurts terribly.”

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