He made three significant changes from the team which beat Denmark to finish Group B with a 100 per cent record, the stand-out one being replacing three-goal striker Mario Gomez with Miroslav Klose.
Low said he was unconcerned these alterations leaked out into the public domain hours before kick-off, even if it did somewhat spoil the element of surprise.
After missing a host of first-half chances, captain Philipp Lahm gave the three-time champions the lead just before the break.
Even though Celtic striker Georgios Samaras equalised soon after the interval, goals from Sami Khedira, Klose and Marco Reus eased Germany into a last-four encounter with England or Italy despite Dimitris Salpingidis’ late penalty.
"To be cheeky is a good thing. Today it was the time to bring in some fresh faces and different types of players who could do a job and I think it worked very well," said Low.
"I thought after three victories, with which I was satisfied, we needed to be unpredictable against Greece because they know us very well."
On his line-up being made public earlier today, he added: "It is not the way I would have wanted but it is the way it happened and that is that."
Regarding the game itself Low said: "I don’t think there is any question we absolutely deserved to win this match.
"Greece scored two goals out of one chance and the only thing I can say is we didn’t take chances at the start of the game.
"Right from the start we were very good, we had lots of chances.
"They had a strong defense but in the second half we didn’t let them hassle us because of the goal we conceded.
"We put in a good performance and the whole way we played was fantastic."
Greece coach Fernando Santos admitted his side were smothered by Germany – who dominated possession – in the first half, but was pleased with their showing after the interval and also overall at Euro 2012.
"I would like to congratulate Germany. They played well," he said.
"I would also like to congratulate my players not only for today’s performance and effort in today’s match but for all their efforts during this tournament.
"The German team were really good and they deserved their huge percentage of ball possession.
"We could have maintained possession more and could have taken more chances but we didn’t have the space to breathe. And given Germany had the ball most of the time they could actually press us towards our goal.
"Despite our defensive efforts we conceded a goal.
"At half-time we told them we had to correct some minor mistakes and try to take more initiative in attack.
"We told them if we could score once it would change the game completely.
"We managed to score and create chances but we conceded the second goal really soon afterwards and that clipped our wings.
"After that it was really difficult to get back to the game. No matter how good your defense is after a certain point you become tired.
"But if someone had told me we would score twice against Germany I would never have believed them."