Costa Rica coach Jorge Luis Pinto praised his players.
"We are not a world football power but we have done very important things here," Pinto said. "When it comes to penalties, you have to understand the player, the pressure and the circumstances they are in.
"We did a great job."
Pinto, whose side surprisingly finished ahead of Uruguay, Italy and England in the group stages to progress to the knock-out rounds, admitted the Dutch were the better side.
"We were lucky throughout the game," Pinto said. "Navas was brilliant and spectacular.
"We go home proud of what we have done and I want to express my gratitude to the Brazilian people."