The Germans crushed Australia 4-0 on Sunday in Durban but Bierhoff was still not satisfied as they took early control of Group D.
"It would be wrong to rest on our achievements against Australia and I am sure we will lift our performance up a notch against Serbia. We just have to," the former Germany striker said ahead of their next Group D match on Friday.
"We have to improve our conversion of chances. There was some carelessness there (against Australia)," he told reporters on Thursday. "We have to be precise and unforgiving when our opponent offers us the chance."
Germany did squander some good opprtunities to add to their goal tally against Australia but their overall performance won them widespread praise and earned their young squad much-needed respect.
WRAP UP
Germany take on wounded Serbia in Port Elizabeth, eager to wrap up their qualification with a game to spare.
Serbia lost their opener to Ghana 1-0 and are in need of a win to keep their realistic chances of qualifying alive.
Bierhoff, however, warned his players not to be complacent.
"We do feel this euphoria but we have not achieved anything yet," he said.
"We do not want to have our third game against Ghana turn into a knockout game. We want to avoid that," Bierhoff said.
Midfielder Bastian Schweinsteiger has all but overcome a minor cold, triggered by the sudden and sharp drop in temperatures, and trained with the team at their Atteridgeville pitch near Pretoria on Thursday.
"We must raise our game further against the Serbs, who I think have called this match 'the game of the century'," said Bierhoff. "So we have to consider ourselves warned."
Germany's final group match against Ghana is on June 23 in Johannesburg's Soccer City.
