Victory over the Springboks equalled world champions New Zealand's national record of 17 test wins in a row and gave them a clean sweep in six matches in the Rugby Championship.
The All Blacks will be chasing an 18th straight triumph when they meet Australia in the Bledisloe Cup in Auckland on October 22.
"There is a real determination to try and improve every time we play," Hansen told reporters after his side racked up nine tries. "We work hard on trying to play a good brand of rugby and at the same time win test matches so we are not playing silly rugby.
"At the moment it's working for us, I'm very proud of them. We planned very well for the World Cup and beyond - I'm not saying the others haven't but we have.
"We put a lot of work into making sure we had a captain [Kieran Read] at the ready to lead and he has done that magnificently. We planned for knowing we were going to lose a lot of test caps [to retirement]," added Hansen.
"I can't explain why the others haven't kicked on but I just know that is the reason why we have managed to stay where we were, or even got a little bit better."
Winning breeds confidence and Hansen said his players had tremendous self-belief.
"Some of those tries tonight were outrageous. When you get to a point where you really believe in yourself ... they want to play, they want to express themselves and they are learning game by game when to do that better."
Hansen said, though, that victory over Australia later this month was no certainty.
"If we are going to make sure we go one step further then we have to prepare well," he said.
"Australia are a really good side, they have a history of turning up when there is a record on the table."