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."
"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.
"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.
