The Central American nation bravely forced a penalty shootout after keeping the more-fancied Dutch at bay for 120 minutes in Salvador, with extra-time ending 0-0.
Navas tallied seven saves as he ensured Louis van Gaal's men remained scoreless, but he could not keep out any of the Netherlands' four penalties - with the fresh Tim Krul, substituted on late in extra time, the difference at the death.
Regardless of their exit, Navas said their Brazil campaign was a success.
"This World Cup has been a great experience and we're leaving with our heads held high. Everyone did a good job," Navas said, as reported by FIFA.com.
"We left everything on the pitch. Nobody likes to lose and it's hard. We didn't lose any game - a penalty shootout isn't a defeat."
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