Löw: Cup within Germany's grasp
"There is still a lot for us to achieve," said a calm Low, following the three-time winners' mesmerising 4-0 trouncing.
"There are still two matches to go. We have got it in our own grasp to win the big prize," the 50-year-old told reporters.
Germany, who won the title in 1954, 1974 and 1990, looked sharper against their much-fancied opponents, whom they also beat at the same stage of the 2006 tournament on penalties.
But spot kicks were not needed this time as Germany outran, outsmarted and outclassed Argentina, making them look like a team past their best.
"Our players are younger, faster. Some of the Argentine players perhaps do not have this speed anymore," said Low, who in his first World Cup in charge has already seen Germany's youngest World Cup team since 1934 fire four goals past England and Argentina.
"In today's victory we were highly disciplined, but we were also willing to put in the extra effort," he said.
After 20-year-old Thomas Muller put them ahead in the third minute with a glancing header, the Germans stepped on the gas in the second half with Miroslav Klose adding one either side of an Arne Friedrich goal.
"We knew at half time we would need to get a second goal because we knew Argentina would put a lot of pressure on us in the second half," he said.
"I am very proud of this team, the great way we played in the second half was first class. The team played like champions," Low said.
Germany will now play either Spain or Paraguay in the semi-final, with the two meeting later on Saturday in the last quarter-final.
"I hope we meet Spain next, they are favourites, an excellent team," said man-of-the-match Bastian Schweinsteiger, who set up the first goal with a curled free-kick.
"We lost to them two years ago in the (final of the) European Championship and I always enjoy most playing against top teams," he said.