The Kiwis reaffirmed their stature in world rugby with a dominant 51-20 win over Australia in the Rugby Championship on Saturday while the Springboks squeaked past Argentina 33-31.
And Warburton, who captained the Lions in the first two Tests of the successful tour to Australia in 2013, admits recent Wales performances have not been up to scratch.
"To be brutally honest, we haven't been quite good enough," Warburton told Wales Online.
"We are the only home nation not to have managed it in recent years. That is something we have to rectify. We need to get that monkey off our backs.
"We've been close, very close four or five times against Australia. But close is not good enough. You can't claim you are unlucky five times."