It can’t have been easy counting, especially after 2,900 litres of free beer had been dispensed to the crowd. Estimates in the end ranged from 4,000-7,000 attendees, but it was impossible to put a number on the delirious joy with which the FC Augsburg supporters and the team celebrated, at the city’s central square, the unlikeliest Bundesliga success story in many years.

Little FCA, run on a budget of around €20m, stuffed with journeymen, sandwiched right in the middle between Stuttgart and Bayern, have qualified for the Europa League in their fourth season in the top flight – in fifth place, ahead of the Champions League regulars Dortmund and Schalke, courtesy of a 3-1 win at Borussia Mönchengladbach on the final day of the season. “In Europe, nobody know us,” the slogan on the team’s T-shirts proudly declared, in slightly more colourful language in the German original. “This is the best team Augsburg have had in 100 years,” the president Klaus Hofmann declared, quite rightly.

The city’s mayor had said that he would let the team back on to the municipality balcony for a second time after their promotion in 2010 if they qualified for Europe but probably never dreamt that he would have to keep his promise. Every single fan interviewed by local radio, TV and newspapers expressed incredulity. They had braced themselves for another relegation battle this season, not the draw for the group stage of Uefa’s second competition.

It’s a frankly stupendous achievement, born out of a bit of good fortune. Sascha Mölders scored with his backside to secure a 3-2 win at Fortuna Düsseldorf – the beginning of a miraculous fightback after the first 17 games of the 2012-13 season had left them 17th place with only nine points, and the veteran Alex Manninger later that year saved a penalty from Fürth’s Edgar Prib in the last game of the campaign at the second time of asking, to help his side to the 3-1 win that kept them up. The referee had ruled out Prib’s first successful attempt.

The club’s persistence with the coach Markus Weinzierl two years ago, despite his disastrous start to life at the top level – he had only trained Jahn Regensburg in the third division before – wasn’t just good luck, however, but a far-sighted masterstroke. In his second season, the former Bayern Munich player took Augsburg to eighth place. They lost their one true outstanding player, the Germany international André Hahn, to Borussia Mönchengladbach but that didn’t stop them outpacing the two Ruhr clubs, as well as all of the other traditional Europa League hopefuls this season. “We are over the moon that we have managed to put the icing on the cake for the whole season with a fantastic performance,” said Weinzierl.

Statistically, Augsburg’s success is quite hard to explain. None of their numbers truly stand out. They have scored 43 goals and conceded 43. They have won 15 games, drawn four and lost 15 games. Their passing numbers are in line with the league average, along with their won tackles and running distance. They have won many tight games but you can’t detect heightened levels of efficiency in front of goal. Nearly seven shots per goal scored is an unremarkable figure. The only number pointing at their special durability is 288 opposition shots at their goal. Only Bayern (177), Leverkusen (194), Dortmund (206), and Wolfsburg (243) have awarded opponents fewer chances to score. Weinzierl has made the maximum of very little.

You sense that the players themselves aren’t quite sure how their sensational season has come about. “Augsburg in fifth place – it’s sheer madness,” said Pierre Hojbjerg, the midfield-loanee from Bayern. Halil Altintop spoke of the special family atmosphere and togetherness at the club, and it’s true; their dressing room is free of egos, a prerequisite for the manager’s blue collar style of pressing hard in midfield. But a huge part of what’s happened in the SGL-Arena, a snug 30,000-seat stadium that still has to make do without a facade after its opening next to the motorway in 2009 – the club have preferred to put the €3m into the team instead – cannot be explained rationally, beyond the basic notion that Augsburg’s competence has been enough to make them extraordinary in a season where most of the big guns have misfired to varying degrees. It’s a very German fairytale, this: the story of a job simply well done.

Talking Points

• “Job well done” will also be the epitaph of Huub Stevens’ second spell in charge at VfB Stuttgart. The Dutchman managed to save the Swabians for a second time in as many years with a 2-1 win at Paderborn that took them to 14th in table. They had spent the entire second half of the season in the relegation zone. The 61-year-old is off to Mallorca on holiday, where he might well bump into Jürgen Klopp soon – Alexander Zorniger will take over for the next campaign. Stuttgart have Stevens’ calmness and surprising tactical flexibility to thank for avoiding a first relegation since 1975: the former clean-sheet fetishist suddenly discovered the joys of attacking football, and allowed the talented forwards Daniel Ginczek et al to strike down the monsters in the basement. “It was difficult but also a fun time,” Stevens said before jetting off into the sun. His phone will surely ring again, come January, but hopefully he won’t be tasked to go for a hat-trick. Stuttgart have a good enough squad to get back into Europe next season.

• Klopp was given a typically rousing send-off by the BVB fans before Dortmund’s 3-2 win over Bremen; a result that guarantees Europa League football for the Black and Yellows. The manager had not trusted himself to deliver a live address to the crowd – “I did that a few years ago at Mainz and didn’t understand a word I was saying” – and instead recorded a video message. A second, more emotional speech is scheduled for the day after the cup final against Wolfsburg.

• There were of course tears at Paderborn after a relegation that had looked anything but inevitable after the first half of the season, which had seen them go into the winter break in 10th spot. “It was unnecessary,” said their coach, André Breitenreiter. The Westphalians will rebuild without haste. SC Freiburg, the second team to go down with them following their 2-1 defeat at Hannover, are also one of the better positioned clubs to deal with the demotion. But that will be scant consolation after spending six years in the top flight.

“Disbelief and sadness will really kick in the next few weeks,” said Freiburg’s coach, Christian Streich, who was especially upset after rival officials had patronised his side in the wake of their 2-1 win against Bayern Munich last week. “Others are being rewarded for their unsporting behaviour,” said the 49-year-old, before withdrawing to a tearful dressing room, “nobody is talking about Schalke losing against Hamburg.”

Well, people at Schalke did. The lifeless 2-0 defeat by HSV was the final straw to break the back of Roberto Di Matteo in Gelsenkirchen. The Italian will officially get his marching orders after seven spectacularly underwhelming months in charge. In truth, his results were not that terrible, but the team’s performances were, almost without exception. In addition, suspicions had grown that his cool, distant demeanour was not hiding deep thoughts on football but actually very little. “It was impossible to say what kind of idea he stood for,” wrote Kicker.

• HSV’s 2-0 win against the Royal Blues consigned Paderborn and Freiburg to automatic relegation and gave Bruno Labbadia the opportunity to repeat this side’s relegation play-off survival act from last season. Karlsruher SC will be the opponents on Thursday and Monday. “We need two more big efforts but we’re no longer dependent on others, that’s good,” said the manager.

KSC won’t be nearly as accommodating as Schalke, however. And neutrals will look at the tie with mixed emotions. On the one hand, Hamburg truly deserve to drop a level for years of chaos and capricious transfer dealings. On the other hand, they are one of the biggest names and it would hurt to see their unique talent – forever making a spectacle of themselves – being wasted in Bundesliga 2.

Results: Bayern 2-0 Mainz, Hoffenheim 2-1 Hertha, Dortmund 3-2 Werder, Hamburg 2-0 Schalke, Hannover 2-1 Freiburg, Frankfurt 2-1 Leverkusen, Köln 2-2 Wolfsburg, Gladbach 1-3 Augsburg, Paderborn 1-2 Stuttgart.