For the second game running Gareth Evans' side lost three first-half goals, and Norway added two more in the second period. The Scots finished third in the group, ahead of Belgium.
First-half goals from Marit Clausen, Lisa Naalsund and Synne Hansen did the damage as the Scots struggled to cope with the searing conditions.
Scotland pushed forward in the second half seeking the goals that would give them an outside shot at qualification, but they were made to pay for their cavalier approach when Marie Markussen and Synne Jansen struck to end their hopes.
Evans made one change from Friday's 3-2 defeat to the Netherlands in Jessheim. Georgie Rafferty, who came on for the second half against the Dutch, started alongside Rachel O'Neill at centre-half but, unfortunately, the Scots found themselves two goals down after 20 minutes and never looked like getting back into the game thereafter.
Norway and the Netherlands, who defeated Belgium 2-0, progress to the semi-finals, along with the Republic of Ireland and Spain from Group B but Scotland exited with their heads held high after recording their best ever finish at a finals tournament.