"We have to be hitting our straps going into that game against New Zealand. We have to play smart and not be frantic when we're holding possession," Williams added.
In-form USA midfielder Michelle Vittese said her team, which remains winless and at the bottom of the table after four rounds, was a bit soft and didn't convert.
"Not getting three cards, like we did, will help us too. We have to manage that."
Australia took a 1-0 lead courtesy of a field goal from midfielder Jane-Anne Claxton seven minutes into the first quarter. It followed a scramble in front of the goal mouth.
The second quarter was more even territory wise. Aussie failed with a penalty corner attempt in the second minute.
The United States were unlucky not have an own goal awarded in their favour with five minutes remaining. Some superb saves from Aussie goal keeper Ashlee Wells saw the score remain 1-0 to her team at the halftime whistle.
The United States had two players, Michelle Vittese and Taylor West, green carded at the same time during the third quarter but still managed to keep the Aussies out with keeper Lauren Blaxing having some memorale patches. The United States equalised when Kathleen Sharkey converted a penalty corner with two minutes remaining in the third quarter.
The Aussies appeared to be tiring in the fourth quarter but took the lead with 12 minutes remaining with a field goal from Emily Smith. Two minutes later Ashlea Fey converted a penalty corner to extend the lead.