"We're not getting carried away, we know we've got the world champions in the next game. We're a minnow in terms of football status so we're just going to go and give it our all, put our hearts and see where we go," forward Chris Killen said.
The All Whites, one of the lowest ranked teams of sports' most watched tournament in South Africa, scored a last minute equaliser in the first game against Slovakia.
All teams in the group now sit on one point after Italy were held to the same 1-1 scoreline by Paraguay.
New Zealand should be strengthened by the return of midfielder Tim Brown, with the vice-captain having recovered from a fractured shoulder.
"I'm feeling much better. The team's playing quite well at the moment so it's hard to get back in there but hopefully I'll be fit," Brown told Reuters.
He said the All Whites would give it their all and may well surprise pundits again.
"We're in with a real chance to surprise some people. Our dream of qualifying for the next round is still very much alive and we'll hold onto that for as long as we can."
The reliable 29-year-old, who plays for Wellington Phoenix, could provide more depth in midfield for a team that looked far more dangerous against Slovakia when pushing forward at the end of Tuesday's match.
The All Whites had a good chance of an equaliser a few minutes before the Winston Reid header that secured the point, but Shane Smeltz pushed the ball wide of the upright after an almost identical move.
However, Italy and a Paraguay team that showed against the champions that they are strong contenders to make it through the group stage, may be more difficult to break down.
New Zealand coach Ricki Herbert said the Slovakia game was always the best chance of a point but his team would not give in easily.
"We're in the group, we've got a chance, we're on the same points after round one. Who would have ever thought that?" he asked.
"I can say we have got two big hurdles to go and if they are too big, then they're too big but they will certainly know that they have been in a football match."
New Zealand play Italy on June 20 in Nelspruit and Paraguay in Polokwane on June 24.
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