"The most frustrating aspect of our struggle in the Tri Nations competition is that we all know we are capable of much better," Smit saidr.
"Our most important task this weekend is to play the kind of rugby that made us so successful for two years.
"In this, I have an important task because it is expected of me, as captain, to bring out the best in every player. It is not only a matter of being able to play better - we must do so."
Smit was booed by the Loftus stadium crowd last week as the All Blacks downed the Boks 45-26, but the 28-year-old said he understood the disappointment of the spectators.
He added: "If they feel only half of what we as players feel for the Springbok jersey, it must be heartbreaking to see the national team lose week after week.
"My message to our supporters is that they should, more than ever, get behind the Springboks.
"The present slump is merely temporary. We have shown, during the past two seasons, what heights we are capable of reaching. We'll be back."
If the Boks lose Saturday's game against the All Blacks and next week's Tri Nations finale against Australia, they will officially set the worst losing streak in the history of South African rugby.