Germany bow out with a 2-0 defeat at Wembley, their first loss against England in the knockout stages of a major tournament since the 1966 World Cup final.
Late goals by Raheem Sterling and Harry Kane at Wembley put England into the quarter-finals Tuesday and brought down the curtain on Loew's 15-year reign as Germany coach.
Loew will be replaced by his one-time assistant Hansi Flick, who led Bayern Munich to Champions League glory in 2020, after the European Championship.
A 1-0 defeat to France has left Germany playing catch-up while Portugal top Group F after Cristiano Ronaldo scored twice in their 3-0 win over Hungary in their opening game.
Joachim Loew's Germany lost 1-0 to France in their opening game at the Euro and another defeat against the title holders would leave them facing early elimination again.
A tense 1-0 defeat by France in their opening Group F game leaves the Germans needing a result at the Allianz Arena against Cristiano Ronaldo's Portugal.
Coach Joachim Loew will step down after the European Championship and wants to forge a mentality "like 2014" when his squad "pulled together" to win the World Cup.
Loew led Germany to victory in the 2014 World Cup in Brazil, but their title defence in Russia in 2018 ended in embarrassment as they finished last in their first-round group.
Germany's Nations League clash with the Netherlands on Saturday in Amsterdam will be Loew's 168th international since taking charge in 2006, but Ballack says his 12-year reign should already be over.
Loew said on Wednesday he had failed in his attempts to contact the Arsenal midfielder and that he had been notified of Ozil's international retirement by the player's advisor.
It was the first time since 1938 that a Germany side failed to get past the first round at a World Cup finals -- a huge dent to Loew's reputation after 12 successful years in charge.
Germany needed to beat South Korea by two clear goals in their final group F match in Kazan to advance to the last 16.
Germany have failed to qualify from the group stages at a FIFA World Cup finals for the first time since 1938.
Gary Lineker had to modify his famous quote about the Germans always winning for a second time after Joachim Loew's holders crashed out of the World Cup on Wednesday.
Germany qualified for Russia with a perfect record of 10 wins, but Hummels said the last time the team played well was when they wrapped up qualification late last year.