Die Mannschaft are set to square off against Algeria in the round of 16 after topping Group G and Low, whose current deal expires in 2016, maintains that he has the support of the German Football Association (DFB).
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Low also seemed focused on ignoring "exaggerated" criticism of his management, having failed to win any honours with Germany after eight years in charge.
"If you differ [from winning titles], you will be questioned and be criticised but, over the course of time, I find it [the criticism] exaggerated and shameful," he remarked.
DFB president Wolfgang Niersbach backed Germany's standing under Low and rejected the suggestion that his continued appointment would depend on his results this summer.
"We extended the contract of Joachim Low with the clear intention that he stays until 2016," he declared.
"There is a very clear agreement [between me and Low]. There are no clauses included in the deal that hinge on results. Our team still has bright prospects, especially for Euro 2016."