The Dutch suffered the disappointment of being beaten finalists for the third time four years ago in South Africa as they lost to Spain, and they have never lifted football's most-coveted prize.
But Robben and his team-mates are out to change that in Brazil, where Louis van Gaal's men have won each of their four games thus far en route to the quarter-finals.
The Bayern Munich winger told FIFA.com: "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."
Such spirit has certainly been on show thus far, with Netherlands reaching the last eight - where they will face Costa Rica - thanks to a dramatic comeback against Mexico.
Two-one down after 87 minutes, Van Gaal's side turned the game on its head thanks to a fine strike from Wesley Sneijder and substitute Klaas-Jan Huntelaar's last-ditch penalty.
Robben puts much of the credit down to the head coach, who will take the reins at Manchester United at the conclusion of the tournament.
He added: "We have a fantastic manager who knows exactly which players to bring on at what time and how to change things on the pitch, so that's fantastic."
