"It's over: The Oranje won't go to the World Cup final after penalty drama with Argentina," popular tabloid Algemeen Dagblad said on its website.
It called the match a "chess game", saying the "tempo was too low, with few chances to score."
The Dutch "failed to launch" dual attack force Robin van Persie and Arjen Robben, the paper added.
"Oranje defeated" popular daily broadsheet De Telegraaf said, with a photo showing Argentine goalkeeper Sergio Romero's save against Ron Vlaar, who took the first penalty.
"It was a nerve-racking game of chess. But so, after five wins the Brazilian adventure comes to an end," it said.
Ajax Amsterdam's club coach and former Dutch international Frank de Boer questioned the decision to let Vlaar take the first penalty rather than a more experienced player.
"Vlaar should not have taken it," he told the NOS public broadcaster.
"But that's my only criticism, we can be very proud of the Orange 11," said De Boer, the Netherlands' most-capped outfield player -- who himself missed an important penalty kick in a semi-final shootout at the 2000 European Championship.
The miss led to a defeat against Italy.
Although many players and coach Louis van Gaal dismissed Saturday's third place play-off against Brazil, some commentators said the loss may prove a blessing in disguise.
"Perhaps it's better that we don't meet the Germans in the final," one commentator told NOS shortly after the game. The Germans and Dutch are neighbors and longtime sporting rivals.
Germany demolished hosts Brazil 7-1 in their semi-final on Tuesday.
Argentina, chasing their third World Cup title, last reached the final in Italy in 1990, when they lost 1-0 to West Germany.