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The 2014 World Cup winners were knocked out by England in the round of 16, with the 2-0 defeat the first time Germany have been beaten by the Three Lions in a knockout competition since 1966.
Germany won just one game out of four and conceded seven goals, despite playing a back five in every outing.
Muller, who was guilty of missing a golden chance to level matters against England, feels Germany's approach was all wrong.
Thomas Muller misses the target entirely on a 1-on-1 chance with Jordan Pickford. Unbelievable. pic.twitter.com/7NfhuTYr0Q- Matchday365 (@Matchday365) June 29, 2021
With our efforts to keep clean sheets with our rather hesitant, compact, defensive tactics, we have de facto failed," the Bayern Munich star wrote in his monthly newsletter.
On Instagram, Muller issued an apology for his miss against England - which came minutes after Raheem Sterling had opened the scoring at Wembley.
Muller was substituted for Jamal Musiala in stoppage time and looked incredibly angry after being taken off.
Recalled and brought back into the Germany fold following an extended absence, Muller is still yet to find the net in 15 European Championship appearances.
However, he says he will use the negative of being knocked out of the Euros and turn into a positive going into the season with Bayern.
"I always try to turn a sporting disappointment like this into additional positive energy," he added.
"As always, I want and have to prove myself. I generally have motivation and ambition to a sufficient degree."
Former RB Leipzig coach Julian Nagelsmann, 33, will be Muller's new manager at club level after Hansi Flick was appointed as Low's successor in the German national team set-up.
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