Los Ticos were knocked out of the tournament after losing 4-3 in a penalty shootout, having held their opponents to a goalless draw.
Navas has admitted that it was tough to lose on penalties, but he believes that his teammates can return home from Brazil proud of their achievements.
"We're left with an empty feeling," Navas told reporters. "Lots of things go through your head. I think we all did a great job.
"It's hard to lose, no one likes it. But this team can leave with their heads held high. We didn't lose a single game. We lost on penalties. It's hard but that's life."
Navas has made 58 appearances for the Costa Rica national side.