Their main attacking weapons have been the left boot of Percy Montgomery and winger Bryan Habana's searing pace.
"We need to be as ruthless with the ball in hand as we are without the ball," White said.
"We are almost content waiting for the turnover, but we don't seem to have the same switched-on approach that we have when we don't have the ball.
"It's something the team knows if they want to improve as we go along. They have to be as focused with the ball as they are without the ball."
The expected damp conditions in Dunedin could create the sort of turnovers the South Africans have prospered from.
"It's going to be a bit slower," admitted White. "Carisbrook at 7.30pm has a lot of dew. It won't be as open and that's obviously the style we are going to play."