Denmark topped Group H with 19 points, three ahead of Portugal and Norway, and they started strongly with Michael Silbarbauer tipping Christian Eriksen's free-kick into keeper Rui Patricio's goal but his effort was ruled out for a foul despite the Danes' celebrations.
"The qualifying round is all about form. We struck it today and hopefully we will be able to find the same quality next Summer," said Olsen.
Portugal struggled to overcome Denmark's possession but they lacked aggression, looked vulnerable at set-pieces and long balls and rarely threatened.
"We didn't play a good match, lost calm in an initial phase of the game and had difficulties linking our game. We were not dominant from the start of the game has we intended to," said Portugal coach Paulo Bento.
Denmark captain Thomas Sorensen was proud of his team's performance.
"We were playing against two of the best wings in the world, but we didn't see much of them for almost the entire match. We are a proud group of guys right now," said Sorensen.
The home side, who won the 1992 European Championships, only had to wait until the 13th minute go ahead, however, when midfielder Krohn-Dehli cut in and fired a curling shot past Patricio.
Portugal struggled to overcome Denmark's possession but they lacked aggression, looked vulnerable at set-pieces and long balls and only threatened in the last 10 minutes of the first half.
Cristiano Ronaldo first saw his diagonal low shot well held by Sorensen on 38 minutes and moments later Nani could have leveled but his shot went just over Sorensen's bar in two rare moments of danger inside Denmark's box.
Ten minutes into the first half Nani jinked past two defenders on the right and layed it for Carlos Martins, whose left-footed shot inside the box was safely caught by Sorensen.
Portugal lacked speed in attack and were shaky in the back throughout, struggling with the Dane's physical game and acute tactical organization.
Denmark's second came when veteran Dennis Rommedahl punished Portugal on the break, racing past left-back Eliseu on the right wing to square for a simple tap-in by Bendtner on 63 minutes.
The Danes could have added a third but were wasteful in attack with both Bendtner and Rommedahl missing good chances.
Ronaldo, ineffective throughout, scored a consolation for Portugal with a trademark dipping free-kick at the start of stoppage-time but it was too late for the visitors who will go into the play-offs.
