RIO DE JANEIRO — When Mario Götze settled a crossing pass with his chest and volleyed a goal that won the World Cup, German fans roared in ecstatic release. Those from Brazil were nearly as delirious, even if it was out of relief as much as celebration.

It might have seemed an odd sight, Brazilian fans celebrating another team inside their own cathedral of soccer, the Maracanã stadium. But after two demoralizing losses brought national embarrassment, solace finally came Sunday as Germany defeated Argentina, 1-0, to become the first European team to win a World Cup played in North or South America.“Argentina winning would have been the worst thing I could think of,” said Jaime Costa, 30, a Brazil fan who works in publicity for a music company.

By the tens of thousands, Argentine fans had crossed into neighboring Brazil, many sleeping in tents and mobile homes and taunting their chief rivals by singing, “Brazil, tell me how it feels to have your daddy in the house.” Roughly, that translates as “How does it feel to be bossed around in your own backyard?” Brazil lost, 7-1, to Germany last Wednesday in the semifinal round — its worst defeat ever — and then appeared feeble again in a 3-0 loss to the Netherlands in Saturday’s third-place game. Meanwhile, Argentina had reached the final for the first time in 24 years, led by its star Lionel Messi, widely considered the best player in the world.“We hate them, and we don’t even know why,” said Flávia Torezani, 31, a computer programmer from Brazil who cheered herself hoarse at Sunday’s outcome as Argentine fans and players faced the heartbreak of narrow defeat. “They’re our rivals. We don’t want them to win, ever. This was almost like Brazil winning today.”

Sunday’s final concluded a monthlong tournament that presented a jarring contrast between Brazil’s hosting of the tournament and its achievement on the field. The World Cup was well organized despite fears that it would be chaotic. The Brazilian people were hospitable. The soccer was largely attractive and attacking. Some have called this the best World Cup in recent memory.

Soccer became so absorbing that widespread protests — against perceived wasteful spending on the World Cup and the 2016 Rio Olympics — did not occur after undermining a warm-up tournament last year.

Yet Brazil’s hope of winning a sixth World Cup ended in humiliation with that semifinal loss to Germany. The country was stunned. It was as if some essential truth had been altered. Brazil not only could be beaten at home, it could be routed and demoralized.“It has left a terrible blemish, a deep scar,” said Aldo Rebelo, Brazil’s sports minister. “It was a disaster.”

After the loss to Germany, Brazilians reacted with mordant humor: Another goal was found in the shaggy hair of the Brazilian defender David Luiz. Not even Volkswagen could produce Gols — a popular model it builds here — as quickly as the German national team could produce goals. Messi would not play Sunday because he got stomach problems from laughing so hard at Brazil’s defeat.Before Saturday’s third-place match in Brasília, the capital, fans welcomed the national team with heartfelt cheers. But things fell apart rapidly, and the response was morose. Romário, the star of Brazil’s 1994 World Cup championship team and now a politician, suggested that most current players never be allowed to wear the national team jersey again.

Thiago Silva, Brazil’s captain, issued an apology to the nation, saying: “It is a moment of great sadness. It is difficult to go home and say to your family, ‘Sorry, I didn’t manage.’ ”Brazil’s performance as host, however, brought words of encouragement from Olympic officials about the staging of the Rio Games in two years, even if preparations will very likely be completed at the last minute, as they were for the World Cup.

“I think that the world has seen the organizational skills of Brazil in this World Cup,” Thomas Bach, president of the International Olympic Committee, told reporters. “Many were surprised, but you could see how well this went.”

Pedro Trengrouse, a professor of sports management, marketing and law at the Getúlio Vargas Foundation, a Brazilian institute of higher education, said the soccer defeats would not affect Brazil’s self-confidence. After all, it has won five World Cups, more than any nation. And its fourth-place finish here was its highest since it won the World Cup in 2002.

“This will not diminish us as a nation,” Trengrouse said Sunday in an interview.More important than the disappointment, Trengrouse said, is that Brazil’s staging of the tournament is considered a triumph.

“It was a huge success for Brazil and its image overseas, and Brazilians are very proud of this,” Trengrouse said. “That outweighs the impact of the losses.”

In another sense, Brazil’s failure signaled a democratizing of soccer at this World Cup. Costa Rica, for instance, reached the quarterfinals for the first time and came within a game — a loss to the Netherlands in a penalty shootout — of the semifinals.

“In current football, anything can happen,” Raul Meireles, a midfielder from Portugal, said early in the tournament. “There are no easy games. I don’t think there are favored teams anymore.”In the end, two international powers met in Sunday’s final. And at least among Brazilian fans, the outcome was deserved and jubilantly received.“Germany beating us, 7-1, was still better than Argentina winning today,” Juliana Nunez, 19, a day care worker, said at Copacabana Beach in Rio.

Those wearing yellow and green jerseys, Brazil’s colors, cheered loudly aMaracanã when a goal by Argentina was disallowed after an offside call in the 30th minute. They pumped their arms when Messi rolled a shot just wide in the 47th minute. And they hugged when Götze scored the winning goal in the 113th minute.

“I’m very happy,” Alex Domingues, 17, a security worker, said near the stadium. “We didn’t want Argentina to take the title in Brazil. It would have been a national shame.

 
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