Despite the presence of Lyon star Ada Hegerberg in their line-up, 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 quarter-finals 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.
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.
As Norway head home, Austria can looking forward to playing eight-time European champions Germany in the quarter-finals at Brentford on Thursday.