Sarah Zadrazil, who scored Austria's first in a 3-0 rout of Iceland on Wednesday which sealed the historic Group C win.
"That's insane, incredible," said midfielder Sarah Zadrazil, who scored Austria's first in a 3-0 rout of Iceland on Wednesday which sealed the historic Group C win.
"Before the Euros we had supporters but not that many, and right now it's just amazing, what's going on in our country," added the 24-year-old who plays for Turbine Potsdam in the women's Bundesliga.
During Wednesday's match, Austrian TV channel ORF registered a million viewers in the country of 8.7 million people.
Leading the fan chorus, Austrian Chancellor Christian Kern tweeted: "Splendid success - tactical, fast-paced, simply top class. Congratulations to our team."
On Thursday, the Der Standard daily splashed a front-page picture of the team celebrating the win against Iceland with the headline "Austria's female footballers ecstatic with joy."
Der Kurier gushed that "these women are a dream" and the Die Krone Zeitung tabloid said: "The fairy tale continues!"
Football fans flock into Vienna's cafes and cultural centres to watch the games, including the Werkstaetten-und Kulturhaus (WUK) centre, which has installed six large screens and fake grass in its courtyard.
"It's great -- you read things and you hear about things and that makes you proud," midfielder Laura Feiersinger told AFP.
"Our games weren't that popular before the Euros and now everyone wants to watch us."
Both Zadrazil and Feiersinger said team spirit and the "amazing" coach Dominik Thalhammer, in charge since 2011, were key for the success.
"We all work for each other, we're there for each other, we support each other all the time -- the whole team, the whole staff, coaches, everyone," said Zadrazil.
Thalhammer "has done amazing work, we analyze every opponent, we see the weaknesses, we know what they're good at and what we have to do to beat them or to take advantage of their mistakes," she added.
"We have a great coach, he teaches us a lot, and we always want to learn new things, and we try to give our best in every training and in each game we fight for each other," said Feiersinger.
Austria are facing Spain in Sunday's quarter-final, and they will not enter the game as favourites.
"I know they are very good technically, I've watched a lot of their games," Zadrazil told AFP.
"They're a very good team with the ball, but I feel like we have a good team without the ball, we know what we have to do defensively and we'll just try to take advantage of their mistakes."
Feiersinger said the weather might be a factor as Spain struggled with heavy rain pounding the Netherlands in recent days when they played England on Sunday and lost 2-0.
"I think if it's raining it's great for us because we fight every game," said the 24-year-old playing for SC Sand in the women's Bundesliga.
"Maybe they don't like the weather that much so it could be a bonus for us."
In any case, the play-off spot is way beyond Austria's pre-tournament hopes.
"Before the quarterfinals we had very low expectations, we went to the tournament as the underdog and we liked that role because we had no pressure at all and that's how we played every game," said Zadrazil.
"Everything we can achieve now is like extra reward we get out of this hard work we've been doing, and I am just excited for the next game, the next step, and we'll see where we'll end up."
Feiersinger was equally modest.
"That we're playing at the Euros is a huge bonus for us already, and that we reached the quarter-finals is a great success for us," she said.
"We're just happy about the way we've played during the Euros."