The Germans got a third straight win when they beat Denmark 2-1 on Sunday to top Group B in their first ever perfect Euro group stage campaign but it was less convincing than it sounds.
"Three wins, three times narrowly won, three times we trembled," said Niersbach.
"Obviously, it is a top performance by the team. For the first time we got the full nine points in a group stage. I hope we have saved our goals for the quarter-final."
The Germans kept their cool after Denmark equalised as, with Portugal beating Netherlands 2-1 at the same time, another Danish goal would have sent them out of the tournament.
Lars Bender settled German nerves in the 80th minute, scoring the winner in Lviv to set up a quarter-final clash with the 2004 European champions in Gdansk on Friday.
"We have to improve a bit in attack. After three difficult games we can be a bit more focused in the way we prepare," said Germany coach Joachim Loew.
His team, who won all 10 of their qualifiers, have been effective yet have so far failed to replicate the dazzling form of their 2010 World Cup when they scored four goals against England and Argentina in the knockout stages to finish third.
"The game against Greece will be very different. They are dangerous," said the 52-year-old coach.
The three-time European champions, eyeing their first title since 1996, beat Portugal 1-0 and Netherlands 2-1 before their final victory over Denmark but Loew said the Greeks would be a tougher nut to crack and his team would need to up the ante.
Despite German hopes of a comfortable win, their opponents have conceded more than one goal only twice in 24 games.
"No one was counting on the Greeks. They are masters of efficiency," said Loew.
"The Greeks have so far had three scoring chances in the tournament and scored three goals. It will be a good challenge for us to try and solve," he said.