Navas told FIFA.com: "I'm happy and grateful to God for this feeling after another important win for us and the whole country. It was not an easy game at all, and while there were times when we had control, there were also periods when the opposition were on top.
"Obviously being a man down made a difference, but we never gave up. As for my save at the end, I can't remember what was going through my mind.
"All I did was react and keep it out. You can practise penalties and study what the takers do, but I have to hand it to my teammates, who were 100% on target. We're making history and we want to have a place in people's hearts forever."
Costa Rica will face the Netherlands in their quarter-final clash later this week.