Bryan Ruiz's goal proved to be the difference between the two sides and sealed progression for Jorge Luis Pinto nation while Italy need to beat Uruguay to book their place in the next round.
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The veteran goalkeeper says Costa Rica's win is proof that nothing can be taken for granted at major tournaments.
"At the end of the day, we had hoped to do better and do what we had prepared to make life difficult for Costa Rica," he told Sky Sport.
"Instead we had a few more problems than we anticipated and Costa Rica controlled the situation well after taking the lead.
"Costa Rica's qualification was a shock for those who take some things for granted and think there are still weak teams in a World Cup. We've known for several years that there's no such thing as a Cinderella team.
"You get on your feet by looking on the bright side. Even a draw wouldn't have changed anything as we still needed a draw against Uruguay.
"In fact, even a victory would have left us needing a point to be absolutely sure."
Italy's final game is against Uruguay on June 24, with kick-off scheduled at 18:00CET.