As their fans began trooping onto planes long before dawn broke over Munich, few of them cared that Manchester City had miscalculated how many goals they needed to top their Champions League group. That City had beaten Bayern Munich in their own stadium was surely enough.
The fact that Manuel Neuer saved late on from Alvaro Negredo meant that City did not top Group D and that come Monday's draw one of the big beasts of European football will probably await. City cannot draw an English club and nor can they face Bayern again.
That leaves the two Madrid clubs – Real and Atletico, Barcelona and Paris Saint-Germain on the menu. However, given how City have performed, especially at the Etihad Stadium, no beast, however big, will be entirely sure of its survival.
Before Bayern's first match against them in October, the German club's coach, Pep Guardiola, predicted that, should they qualify from the group, City might run wild in the knockout stages.
The way Manuel Pellegrini's side turned what after a dozen minutes looked as if it would be an evening of abject humiliation into Bayern's first defeat in nine months suggests Guardiola could be right.
"We will take anyone in the next round," said James Milner, who won a penalty and scored the winner as people stopped looking up City's heaviest European defeat (only 3-1 to a variety of German clubs) and began wondering when Bayern had last lost (in March to Arsenal).
Joe Hart, for whom this might have been a humbling, career-defining evening, showed the character on an icy Bavarian night that might help him for England in a more humid one in Manaus.
"It has to be up there as our best European moment," said Milner, who gave the kind of driven, against-the-odds performance that England will need in the World Cup. "You have to look at the way the game went, with us being 2-0 down and starting pretty poorly. We had to show character to turn that around.
"This could not have been any tougher. Bayern are the reigning champions and have been to three European Cup finals in the last four years or something ridiculous like that. The real us came out; it was a different team in those first 15 minutes, when we were sloppy off the ball and on it. Now we will know we can progress."
Progress is a key word for City's senior management team of Ferran Soriano and Txiki Begiristain. Frankly, it does not matter overmuch whether City qualified in first or second place so long as they went through, something Roberto Mancini had not managed.
It was neatly ironic that Mancini should have seen his Galatasaray side eliminate Juventus in the snow, slush and mud of Istanbul to finally make it through the sort of group of death that had invariably confronted him in Manchester.
Pellegrini would not have been human if he did not feel a little taken aback by the headlines that in one case proclaimed him a "Blunderboss" for failing to realise that a fourth goal would have sent City through in first place. Bayern had conceded one goal in 11-and-a-half hours of football before Tuesday night and, unlike City, were at full strength. Even had Pellegrini thrown on Sergio Aguero, there was no guarantee he would have scored.
Nevertheless, in a sport where every player's step on a pitch is analysed, it seems astonishing that nobody on the bench at the Allianz Arena realised that 4-2 would be enough.
Compared to South Africa's cricketers, who were eliminated from their own World Cup in 2003 because they failed to understand what score they required under the Duckworth-Lewis system, the consequences were minor.
Alan Ball never lived down the moment in May 1996 when he ordered Steve Lomas to waste time at the end of the 2-2 draw with Liverpool not realising City needed to win to avoid relegation.
Ball had been misinformed by a spectator about other scores and, when he realised the mistake, he "dashed down the track at Maine Road trying to get another message through, no doubt looking like an absolute fool." It was, Ball said, brought up every time he returned to Manchester. The city will be rather more forgiving of Pellegrini.
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