After taking maximum points from their group, die Mannschaft are being tipped for progression to the semi-finals but the coach says they must improve to beat the Euro 2004 winners
Die Mannschaft marched through the so-called 'Group of Death', making a mockery of that moniker with three wins from three against Portugal, Holland and Denmark.
"We've taken nine points from a tough group, against top-class opposition," Low told bundesliga.de.
"All-in-all, that's a fine achievement. But we can, must and fully intend to improve further. This is just a stage on the way to our final target."
After their strong start to the tournament, the Germans - runners-up in 2008 and last winners in 1996 - are strongly fancied to see off Greece in the quarter-finals, the Greeks having surprisingly finished second in Group A, despite winning only once.
Nonetheless, Low does not see the 2004 European Championship winners as easy pickings.
"Not as far as I'm concerned," he insisted.
"Greece are dangerous opponents, they'll try to play deep and take the pace out of the game. They're masters of efficiency - three chances so far in the tournament and they've taken the lot, that says it all.
"We know from the past that they can defend incredibly well - it's like chipping away at granite."
Low was somewhat disappointed with his side's performance in their last match - the 2-1 win over Denmark - and believes that they'll need to be more clinical in front of goal and better organised in midfield to ensure victory.
"We need to be a tad better up front, above all when it comes to taking our chances" Low opined.
"Our movement was pretty good, but we have to make sure the ball finds its target as well.
"On top of that, we sometimes left too much of a hole in midfield and at the back, that's something we need to address.
"We've got until Friday now, when we'll be playing pretty much on our doorstep in Gdansk. So as we don't have to travel anywhere, we'll be able to prepare with a bit more focus."