The Wallabies have won five of the last six Tests against the Springboks stretching back to September 2009 but Smit said his team would look at this weekend's match in Wellington as a fresh start rather than dwell on past results.
"I'm pretty sure they will feel they have a mental edge. The results leading into the World Cup over the last two years certainly favour them," Smit said.
"We'll want to face the game as a fresh start in terms of where we want to go in the next three weeks and I'm pretty sure they'll look at what they've been able to achieve before against us. It's two different mindsets I suppose.
"They certainly have had the upper hand over the last couple of season and we'd be naive not to accept that."
But the knockout stages of the World Cup are a world away from Tri Nations matches and the Springboks' record is pretty formidable. They won the Webb Ellis Cup in 1995 and 2007, finished third in 1999 and bowed out in the quarter-finals in 2003.
They were in political and sporting isolation for the first two tournaments.
Australia's record is not too different. They won in 1991 and 1999, reached the final in 2003, were fourth in 1987 and were knocked out in the quarter-finals in 1995 and 2007.
"The games we've played (in the past two years) have been in a different vein to what a World Cup does provide," said Smit.
"We're both in a situation where it's do-or-die, last chance. We've got to make good on that."
"I suppose they are not going to fool themselves and rely on what they've done and we're not going to fool ourselves and look back at what hasn't been done.
"Each of us are going to take what we've done in the last four weeks and work on that, take the positives out and hopefully put it all together on Sunday."
Smit admitted his side had arrived in New Zealand with little form behind them after resting the majority of the squad for the early stages of the Tri Nations.
But the veteran hooker believed the team were able to build some momentum during the pool phase, where they secured wins over Wales, Fiji, Namibia and Samoa.
"Those pools, especially for us have been invaluable because we came in pretty undercooked," said Smit.
"Having the game time being able to see what your combinations are like and see how players can get into form has been very valuable for us.
"I'm pretty sure it would have been the same for the other teams. Now everyone is on the same level."
Wingers Bryan Habana and JP Pietersen are carrying slight injuries which Springboks coach Peter de Villiers admitted were a worry.
But he was hoping the extra two days off between the bruising win against Samoa last Friday and this Sunday's match in Wellington would be ample time for the players to recover.
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