Los Ticos have been the surprise package of this World Cup, defeating Uruguay and Italy on the way to topping Group D before earning a 5-3 victory on penalties against Greece in the last 16.
Sneijder was quick to reject the suggestion that Oranje would have a simple task against the Central American nation, saying that they have earned the right to be considered among the eight best countries in world football by reaching the quarter-finals.
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"Every match at this stage starts as 50-50. The difference is so little among the teams, anything can happen on a given day and Costa Rica had topped the group sending two European giants, Italy and England, home so there will be too many things to play for."
The Dutch, beaten finalists in 2010, remain among the favourites for the trophy this time around but Arjen Robben added that they must improve from their second-round win over Mexico to realise that aim.
"I thought during the first half we weren't good when Mexico had possession," the winger told reporters. "That will have to improve against Costa Rica.
"In general, I think we were stronger when we had the ball so that's a plus. We have to do that more. We let Mexico play a bit too much.
"I think we are on a mission together and when you come to a World Cup it's not to enjoy the weather and enjoy the beach in Rio. You're here to win matches and to go as far as possible.
"I don't think the expectations were that high before the tournament and as a result we can be very proud of where we are."