Germany went 1-0-2 in the Tournament with their only win coming against Sweden when Toni Kroos scroed the game victor deep into added time. He led the World Cup in saves after the second game against Korea with 14.
Mats Hummels said defending champions Germany's group stage exit from the World Cup finals for the first time since 1938 was a "bitter" shock for the team.
Supporters in the stadium were left fuming with their side's performance, as they failed to get past a Korean side that was billed as one of the worst at the World Cup finals.
Serbia were leading for much of the first half courtesy Aleksandar Mitrovic " s goal in the fifth minute.
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South Korea's win knocked out Germany and allowed Mexico to progress to the next stage of the World Cup - sending the country's fans wild with delight. If they continue to play well the result will come.
Click through the gallery above to see some pictures from Germany's loss to Korea Republic! A 2-1 win against South Korea in their next match strengthened their position at the top of the group.
"The disappointment of being eliminated is just huge", Low added.
Fellow supporter Denis, who traveled nearly 3,000km (1,864 miles) from his home in Stuttgart to watch Germany take on South Korea in Kazan, was equally resigned.
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Sweden's 3-0 win over Mexico in the group's other match meant the pair advanced on six points apiece.
Low and his players will return to Germany on Thursday, but with the coach dismissing suggestions that dark times could lie ahead. Andersson says, "It's important that we're able to move on after that". In 2006, Germany hosted the big tournament but the winners were Italy.
The 55-year-old, who accused Germany's backroom staff of "rubbing it in our faces", also needs to deal with the delicate fall-out surrounding his winger Jimmy Durmaz.
Germany captain Manuel Neuer, Sweden captain Andreas Granqvist, Mexico captain Andrés Guardado and South Korea striker Son Heung-min.
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