The Dutch set up a quarter-final clash with Costa Rica by defeating Mexico 2-1 in the last 16, and the Manchester United man believes that they can go all the way in Brazil.
"Everyone feels we can win it - that it really is possible," The Mirror quotes him as saying.
"To be the captain of this squad makes me incredibly proud, It's a huge honour to be here, at this stage, wearing the armband, because we are a real team.
"All 23 players are important and also the technical staff. The way they prepare for competitions is unprecedented, I've never before known a level like it."
Van Persie has scored three goals in the World Cup so far.