Krul was only brought on late in extra time, before denying Bryan Ruiz and Michael Umana in the penalty shootout.
Coach Louis Van Gaal later revealed that he had told Krul he might bring him on if the game looked like going to penalties - but that he hadn't told first-choice keeper Cillessen.
"There is no question about who will start next game, it will be Cillessen," he said.
"But we felt Krul was the better choice here."
However, it was Costa Rica's keeper Keylor Navas, just recovered from a shoulder injury, who was deemed the man of the match for his efforts in keeping Holland at bay for so long.
The Dutch had plenty of chances, but were either blocked by Navas or hit the woodwork - like a deflected Robin Van Persie shot in the final minute of normal time.
But it is Holland who will face Argentina in the last four, while Los Ticos - who had never made it to the quarter-finals before - who go home.
"We lost everything in a penalty shoot-out and we go home sad but with our heads held high," Navas told Costa Rica newspaper CRhoy.com.
"It's hard but this is life."