Broos's side take on Canada in Los Angeles on Sunday after advancing from the group stage with a surprise 1-0 victory over South Korea, and the Belgian said reaching the knockout rounds had fulfilled the team's initial objective.
"I think we can say already now that the World Cup is a success for us," Broos told reporters.
"Everybody expected and hoped that we should be in the second round. We are in the second round. But that doesn't mean now that we are happy and that we just play the game tomorrow and go home.
"Once you are there, you want more."
Broos said South Africa would need to reproduce the level and mentality they showed against South Korea if they were to overcome Canada, whom he described as a physically imposing side that press aggressively and give opponents little time on the ball.
"They all go for the same goal," he said. "The moment they lose the ball, everyone wants to win it back. That is very difficult to play against."
South Africa, however, have grown into the tournament after losing their opening match to Mexico at the Azteca stadium, with Broos saying the experience of playing on the biggest stage had helped his squad to adapt.
"The first game was very good for us," he said. "Now we believe in ourselves."
At 74, Broos also acknowledged this is likely to be his final World Cup and suggested it could bring the curtain down on his coaching career.
He said he missed his family and grandchildren in Belgium but joked that following South Africa's win over South Korea, his wife had given him permission to extend his stay.
"She said, 'Okay, you can stay another week, there's no problem'," Broos said.
Whether or not it proves to be his final World Cup, Broos said his players were determined to extend the journey by at least one more match.