Australia captain Ricky Ponting called on his side to step up a gear despite beating New Zealand by 96 runs at Port Elizabeth.
Lee ripped through the Kiwi tail
An inspired spell of bowling by Shane Bond saw Australia reeling at 84-7 before Michael Bevan and Andy Bichel pulled their score up to 208-9.
Australia had also slumped to 114-7 against England the last time they played on the slow Port Elizabeth pitch.
And they will have to play their semi-final game at the same venue.
"We don't want to get ourselves into too many of these situations. We lost early wickets again which was disappointing," Ponting said.
If you put the ball in the right spot then you get the rewards
"We are going to have to identify the best way of playing in the first 15 overs when we are batting.
"Both times here we have been four for 40-odd and that is just not good enough."
Australian fast bowler Brett Lee said he was pleased with his performance after taking 5-42.
He polished off New Zealand's lower order after Glenn McGrath had taken three early wickets.
The paceman claimed all five of his wickets in a devastating spell of 15 deliveries.
"It is a pretty flat wicket but if you put the ball in the right spot then you get the rewards," he said.
"The boys all did a great job and I was set up well by Glenn McGrath first up.
"I felt good, especially in the second spell when the ball started to tail in a little bit."