MARSEILLE, France -- After watching her players complete what she called a "mature performance" in their 4-1 victory over Germany here Sunday night, new United States women's national team coach Emma Hayes was typically blunt in describing how she felt.

Her biggest positive? The team's attack, with Sophia Smith scoring twice, Mallory Swanson adding another for her third in two Olympic matches and substitute Lynn Williams closing the scoring to completely stifle any hope of a German comeback.

"I think we were absolutely devastating when we needed to be," Hayes said, after the U.S. win booked her team a spot in the quarterfinals.

Biggest negative? Some poor decision-making that led to Germany having more chances than it might have deserved, with goalkeeper Alyssa Naeher bailing out her teammates after some critical turnovers.

"I thought that we were our biggest problem," Hayes said, adding that six matches into her tenure, "There's still things that irritate me about us, but that's for me to fix."

Hayes then continued that her biggest concern -- beyond the knee injury that forced off Tierna Davidson, who will be evaluated again Monday -- is the emotional recovery that's required in a compressed tournament like this one.

The USWNT plays its final group stage match against Australia on Wednesday, and Hayes is planning to give the team a full day and a half off before returning to the practice field.

"Can you imagine the adrenaline?" Hayes said. "You get so high, the comedown is like any hangover."

Colorful phrases aside, it has been a whirlwind start for Hayes, who only took over the team in June, but now has the Americans into the knockout rounds of her first major tournament. There is still a learning curve, she said, both between her and the players as well as among the players themselves, but there's no doubt that Hayes is working to instill a new identity.

It is a process, she acknowledges, that will take some time. What she saw from her team on Sunday, though, was heartening. The opening half hour was a see-saw, as the U.S. nearly fell behind early after some sloppy defending, only to take the lead, lose it, re-take it again and then stretch the margin to two goals by halftime after Smith scored her second.

"There were times where we had to weather a storm," Williams said. "And I think that that's really cool about this team -- nobody looks frightened in those moments. It's just, okay, what do we need to do?

"It's just more of a belief that no matter what somebody throws at us, we're going to get the job done."

That sentiment is exactly what Hayes is craving. And the determination that the players demonstrated is what she expects.

"There's things I'm learning about the team tonight from a character perspective that I want to see, from a resilience perspective I wanted to see," Hayes said. "When you play a top-level opponent, you get to see all sides and I saw all sides of us tonight, which was pleasing."

The Americans play their last Group B match against Australia on Wednesday and can secure a first-place finish with a draw or a win.