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Low hailed his side's domination of their more experienced opponents as two goals from Thomas Muller and one apiece for Miroslav Klose and Lukas Podolski powered Germany towards a last eight meeting with either Argentina or Mexico.
After the match, a jubilant Low told reporters: "It is a great achievement for our young team to dominate such an experienced English team in such a way.
"It was fun to watch there. We have managed to expose England's defence. Today we played with conviction and courage."
Low also revealed the tactics he used to exploit England's weaknesses. "We knew that the midfielders - Gerrard and Lampard - always support the forwards and that their midfield would be open," he said. "We knew there would be spaces.
"Our objective was to set Terry up with Klose to force him to come out of the defence. We knew the full-backs would be very much to the side, and that would create space that we could penetrate. We could have been 3-0 up in the first half because we did penetrate them.
"We knew that we would have to try and tackle the English early on in midfield and take away any space they would have beyond midfield. We knew they might become impatient and lose their discipline. We did that successfully, but Fabio Capello is very experienced and extremely knowledgeable. I bow down to him."
Low also insisted he had no preference as to who Germany meet in the last eight.
Germany's midfield linchpin Bastian Schweinsteiger said: "I am very proud of this team. We played very well for 90 minutes. We are a good team that still has room for improvement."
German chancellor Angela Merkel wasted no time in offering her congratulations to the national side. She said: "It was a great game and a great victory. I am still very moved. The team can be only be congratulated. I can only say: 'Keep it up'."
Goalkeeper Manuel Neuer admitted Frank Lampard's seemingly legitimate goal "was close", and appeared to acknowledge that Germany were fortunate to escape conceding an equaliser.
"I tried not to react to the referee and just concentrate on what was happening - it was difficult," Neuer said. "I knew it was close.
"Then I saw it on the television in the doping control office and what actually happened. I knew it was tight - probably about two metres!''