The Blackburn Rovers defender, who is captain of the All Whites, wants his side to feed off the support they have been receiving from sports lovers back home more used to cheering on the All Blacks.
Nelsen said: "It's amazing for us. We have felt the support back in New Zealand. We don't usually get this publicity and support. It's humbling and really exciting. We will be making sure we make every New Zealander proud. That is one of our number one goals."
New Zealand did not have the best of warm-ups, losing to Mexico, Australia, Slovenia and Chile, but they did beat Serbia 1-0 two weeks ago.
They are confident of recording the first World Cup finals win in their history, having lost all three group games the only other time they competed in 1982.
Nelsen, who is one of four English league players in the side, the others being Plymouth's Rory Fallon, Middlesbrough's Chris Killen and Ipswich's Tommy Smith, added: "We are very competitive. The reality of World Cup football is that you can play really well and lose all the games but we're a very good team and we want to win. It's as simple as that."
Slovakia coach Vladimir Weiss, meanwhile, is confident his 20-year-old son, also Vladimir, who is with Manchester City, can help his nation progress to the next round in a group which includes Italy and Paraguay.
Weiss senior said: "He is a very clever boy but it is not easy for him because his coach is his father. And he is not an easy player to coach, but I am sure he will show an excellent performance and will help his team. We are all full of expectation."