Despite the presence of Lyon star Ada Hegerberg in their line-up, former European champions Norway paid the price for another lacklustre display in Brighton.
Norway failed to advance from Group A after a second successive loss, while Austria progressed to the quarterfinals as runners-up behind England.
England, already assured of topping the group, crushed Northern Ireland 5-0 in their last game to move into the last eight with three successive wins and without conceding a single goal.
Needing a victory to move above Austria in their final group match, Norway were pushed towards elimination after 37 minutes when Nicole Billa headed in Verena Hanshaw's cross.
The Norwegians were unable to muster a comeback and it was Austria who could have won by a bigger margin with more clinical finishing.
Norway goalkeeper Guro Pettersen made several fine saves to give her side a chance, but Austria's Manuela Zinsberger thwarted Celin Bizet and Hegerberg in the closing stages.
Thrashed 8-0 by England in their previous game, Norway's tournament had quickly turned sour after the initial optimism fuelled by a 4-1 victory over Northern Ireland in their first group match.
"We had higher belief in ourselves than to be out of the tournament this soon. So of course, I feel totally empty," Norway manager Martin Sjogren said.
Former Women's Ballon d'Or winner Hegerberg added: "Everyone has a responsibility in this, myself included.
"There has to be a brutal honesty in evaluating everything that's happened in the last few weeks in order to actually bounce back from this.
"It's almost that I want to apologise because of all the support we've got."
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