Tight, tough quarter-final awaits Matildas
A late Kyah Simon goal saw the Matildas to a 1-0 victory over Brazil in the last 16 on Monday morning (AEST).
Australia return to Edmonton, where they played Sweden in the group stages, for a quarter-final against either Japan or Netherlands on Sunday morning.
Stajcic is aware of the challenge ahead of his team.
Japan beat the Matildas 1-0 in last year's AFC Women's Asian Cup final, while Australia edged Netherlands 1-0 at the Cyprus Women's Cup in March.
"Japan are defending world champions so we know how good they are. They've won every game so far," Stajcic said after his team's win over Brazil.
"We played them in our qualifiers last year at the Asian Cup, we saw a lot of the performance we saw today in the first game we played them. We were 2-0 up but they're a world-class team and they came back and had a 2-2 draw.
"We played them again in the final of that tournament and they like to play in a similar way to us, really good football philosophy, good football culture and it was a great game.
"I'm sure whichever team we play, we beat one 1-0 and lost to Japan 1-0 so whichever way it goes it's going to be a tight game."