You’re not a leopard, and it’s not about spots. In Germany, they believe people can, indeed, change, albeit with considerable effort. One has to “jump over one’s own shadow”, the saying goes.

The German national team have done a lot of jumping since Jürgen Klinsmann and Joachim Löw took over in 2004, with the explicit brief to create a different footballing identity. After the 1-0 win over France in Rio – on a Friday afternoon so hot that the inimitable Thomas Müller described it as “playing in a grill shack” – Oliver Bierhoff seemed all too happy to revert back to a bit of shade, however. The general manager’s praise was peppered with anachronistic, unfashionable words that had become all but banned in a decade’s worth of rebranding.

“We were very organised; we filled in for each other; we were well arranged on the pitch; we were calm; we knew what we had to do to win the game,” said the Euro 1996 winner. “That has always been the strength of German teams.”

Bierhoff was so impressed with his side’s composed performance that he went on to link it to the squad’s “perfect travel arrangements”. The off-pitch organisation had been excellent, the 46-year-old continued, with a hint of self-praise. “Everyone knows where to go, nobody gets lost .” One half-expected Bierhoff to confirm that the hotel rooms for next the final, next Sunday’s final had already been reserved, along with the sun loungers at the pool.

This sort of stereotype-affirmative message would have never come out of the camps in 2006 and 2010; escaping the shadows of their recent past had been their most pressing aim. Germany contested the 2002 World Cup almost as a caricature of itself. A team that seemed exclusively made up of holding midfielders edged out meagre, nervy wins against even more mediocre opposition (Paraguay, USA, South Korea) then came up short against Brazil in the final. Michael Ballack was the one outstanding player, but Oliver Kahn was the hero: the obdurate, consistently grimacing goalkeeper became the unwitting symbol of a team that had stopped playing football and excelled only in negating the opposition.

At the 2006 World Cup in Germany, Klinsmann, his team and the whole country successfully sold themselves as a new, humbler, younger, friendlier version of their former selves, complete with the good grace to let Italy go home with the trophy. Four years later, in South Africa, Löw’s thrilling, multicultural youngsters emancipated themselves even further from results-based football, the minimalistic, ultra-efficient style of yesteryear.

But the Germany fans have grown tired of 10 years of entertainment without a happy end. After the incredibly exciting, but uncomfortably chaotic, 2-1 win over Algeria, the mood was about to turn firmly against Löw. The 54-year-old was in danger of going from his country’s foremost expert – in the public’s estimation – to a stubborn man who was ruining the prospects of a golden generation with his tactical intransigence.

Reaching the semi-final, a record fourth in a row for Germany, was the minimum the supporters expected. “Löw has done it,” wrote Süddeutsche Zeitung. Defeat by Brazil in Belo Horizonte on Tuesday might just be forgivable in the eyes of the fans.

The players see things differently though. They found little pleasure in advancing to the final four. “We have been here before,” the captain, Philipp Lahm, said with an air of world (cup) weariness, “so I don’t want to talk about pride. We need to do it this time.” The 30-year-old angrily dismissed questions about the French team creating chances, saying that “it was natural at this level”.

He, like the increasingly pragmatic Löw, is no longer concerned with football niceties. “Win at all costs”, as chancellor Angela Merkel had decreed in a personal message before kick-off, has become the new motto. It was fitting that Mats Hummels’ winning goal had come from a free-kick. Löw used to sneer at calls for more practice of dead balls – not enough time, he said – but this time, it has become a priority in practice. Efficiency is the new, old watchword. Another one is maturity. “You could see that we have a lot of players who have won the Champions League and know what to do, before and during pressure games,” said Bierhoff.

Listening to Müller – who talked at length about the team’s willingness to run for each other, and their clever game management – it was almost as if the clock had been turned back a couple of decades. Germany were quietly pleased that they had managed to reconnect with elements of their inglorious past in Rio de Janeiro, but not at the cost of forsaking recent progress.

“We are a much better side than in 2010,” said Müller. “We have many more options and can still find another level in attack.” He, and the rest of the squad sounded like men who knew exactly what kind of team they play for. That is more than can be said of some of the other sides – and it might just be enough.