The Springboks face the daunting task of having to win by seven points and score four tries against the world champions at Ellis Park in Johannesburg on Saturday if they are to win the four-nation competition.
Meyer told a media conference in Johannesburg on Monday that the right mind set might yet do the trick for the home team.
"I've always believed whatever the mind can conceive and believe, you can achieve. So we need to go out positively and try and score tries," he said.
"It is a huge challenge and you have to take risks. You either go for the four tries or you don't. That is the decision we have to make. I haven't spoken to the side yet, but I'll definitely want them to go for the four tries.
"It will be very, very difficult because if you go out to score tries the game will open up and they will get opportunities to score. The way they play, they like to put you under pressure and play from your mistakes."
But Meyer added: "We'll have to go for it. There is a chance we can lose the game, but I believe we can't be in two minds. It will be difficult to score four tries against the All Blacks, but if we don't do it - if we don't try - then what is the use of playing?"
Meyer also looked to put a little early pressure on Welsh referee Nigel Owens by suggesting he would need strictly to control the breakdowns, at which South African pundits say New Zealand get away with too many infringements.
South Africa scored only three tries in a 28-8 victory over Australia in their penultimate clash in Cape Town on Saturday, missing out on the bonus point that would have set them an easier task in their final game.