Navas denied Greece striker Theofanis Gekas from the spot as Costa Rica triumphed 5-3 on penalties after scores were level at 1-1 at the end of extra time in Recife on Sunday.
Costa Rica, who were reduced to 10 men following Oscar Duarte's dismissal in the 66th minute, will now play the Netherlands in their first World Cup quarter-final fixture in Salvador on Saturday.
Despite saving the penalty that paved the way for Michael Umana to convert the match-winner, a modest Navas heaped praise on his fellow countrymen.
"I can't remember what was going through my mind," the Levante goalkeeper told FIFA.com. "All I did was react and keep it out.
"You can practice penalties and study what the takers do, but I have to hand it to my team-mates, who were 100 per cent on target.
"We're making history and we want to have a place in people's hearts forever."
Navas added: "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."
