The Welsh side have dominated the last two Six Nations tournaments, and clinched the 2013 title with a 30-3 win over England in Cardiff.
But it is England who have the better record against the southern hemisphere sides, including last weekend's 20-13 win over the Aussies, while Wales have struggled against the Antipodean sides and lost 15-24 to South Africa last weekend.
Warburton wants Wales to follow in the footsteps of both England and the Lions with three wins in the remaining autumn internationals, with games against Argentina and Tonga still to come and culminating in the visit of Australia on November 30.
"England can do it, they can beat these southern hemisphere sides in the autumn, so can we," said Warburton. "And until we do that we can't say we're genuine World Cup contenders.
"People are talking about World Cups already. But if people want to talk about Wales being [World Cup] contenders then we have to beat one of these southern hemisphere countries.