Norway, who are also world and European champions, rounded off a lacklustre group stage campaign by suffering a 25-20 loss to Spain in the penultimate qualifying encounter of the Games.
Group B winners France, still unbeaten, will play debutants Montenegro on Tuesday in the last eight while Beijing runners-up Russia face 2008 bronze medallists South Korea and Spain meet Croatia.
Brazil, seeking a first Olympic handball medal, will get Tuesday's quarter-finals underway.
On a rather subdued day where the quarter-final places had already been decided, there were group positions to play for and the days big losers were Russia, who missed an opportunity to leapfrog Brazil when they drew 25-25 with Montenegro.
Coach Evgeny Trefilov was a constant picture of anger on the touchlines but counterpart Dragan Adzic was understandably delighted with his team's qualification for the last eight.
"It's a great thing for a small country like Montenegro to play at the Olympics, especially to finish equal with a great sporting nation like Russia. We will do our best to win a medal, that's our aim now," he told Reuters through an interpreter.
"Phenomenal. We didn't expect such a handball atmosphere in Britain," he added referring to the crowd at the Copper Box.
Denmark went down 30-24 to France to finish a disappointing Olympics for the three-times winnters.
"We didn't have the luck all the way but we didn't reach our level in this tournament. This team can (give) a lot more than we showed," dejected Danish captain and twice gold medallist Karin Mortensen told Reuters.
"It's part of the game and that's why we are standing here. Ouch."
Coach Jan Pytlick said he would be looking to younger players to return Danish women's handball back to the heights it scaled in three consecutive Games from 1996 when they won gold each time.
"We have to build up the team with young players. I'll have to discuss it with the federation and analyse what is the problem and what we need if we're going to be at the top again."
Emotions were high after the hosts signed off with a 37-14 defeat at the hands of Croatia, players hugging and crying after a rollercoaster ride in front of unseen crowds for handball players in soccer-mad Britain.
The other side to go home without a win were Sweden, beaten 32-28 by South Korea.