Pinto's men led late in normal time before Sokratis Papastathopoulos scored a 90th-minute equaliser to take the game into extra time before penalties ensued.
Pinto told reporters: "This is a big, big result. Words can't describe how I feel right now. It's never easy playing with ten men, and even less so against opponents like that in a World Cup match.
"We looked secure throughout the game, and we were full of confidence in the shoot-out, and that goes for the goalkeeper, who was amazing, and the penalty takers, who were just perfect.
"I'll say it again – we're delighted and we'd like to dedicate this win to all the people of Costa Rica. We respect the Netherlands, just as we respect all our rivals, but the story goes on and we're hungry for more."
Costa Rica take on the Netherlands in their quarter-final clash later this week.