Their early elimination also means that they are the first of the European giants to be knocked out of the competition.
No European team has ever won the World Cup in South America. This, perhaps, is a redundant piece of information; the continent has not staged the tournament since 1978 when, in psychological terms, the planet was a much bigger place. In the age of mass travel, crossing the Atlantic holds much fewer fears than it did in days gone by.
But on the other hand, there are aspects of Brazil 2014 that will test the Europeans more than any previous South American World Cup.
Past tournaments were almost entirely staged in the South Cone, in winter temperatures that range from temperate to bitter. This one, in contrast to Brazil’s 1950 World Cup, features plenty of games in the North East and the North of the country – a region totally untouched by winter.
Worse, for the benefit of a European TV audience, some of these games are being played in scalding afternoon sun, at an hour when no major domestic match would conceivably take place.
World Cup saps energy
A lesson of previous World Cups is that it is a draining tournament. Players and teams can run out of gas in the course of the competition, especially when the matches take place in the heat.
The Netherlands' 3-2 win over Australia, for example, was a marvellously competitive encounter – important to note that it was played in down south in Porto Alegre, which, along with nearby Curitiba, is decidedly cool at this time of year.
But this southern region is part of the supporting cast in this World Cup. Between them, Porto Alegre and Curitiba will stage just 9 matches, and only one in the knockout stages. Meanwhile, the Northeastern cities of Fortaleza, Natal, Recife and Salvador have a total of 21 games, plus another eight for Manaus and Cuiaba.
The level of intensity of the Netherlands-Australia match would be very difficult to reproduce in any of these venues, especially later in the competition when the players are already feeling the effects of previous games.
Two more of the European heavyweights, Germany and Italy, have got off to winning starts. But as the luck of the draw would have it, both will play all three of their Group matches in tropical heat.
They should qualify for the knockout phase, but we will soon find out if they have paid a heavy price for their early exertions. If a European team is to break the hoodoo and win a South American World Cup, thy will have to do it the hard way in Brazil 2014.
Tim Vickery is a South American football correspondent for the BBC and Brazilian football expert.