Stephen Eustáquio scored in second half stoppage time at the Los Angeles Stadium to send the co hosts into the last-16 for the first time.
"Nobody expected us to be in the second round," said Broos. "They only hoped that we'd get there.
"But whenwe look back, I think we we can be very satisfied with what we did at the World Cup.
South Africa last qualified for the World Cup in 2002. Their appearance in 2010 came courtesy of being hosts.
"We have a good mentality and we were able to make good performances and get good results," said Broos.
"I'm still proud of my team. We did it very well in this World Cup even though we're out of the tournament. Iknow why we are out and this is something we have to work on in the next months and years."
Morocco or Netherlands loom for Canada
Canada will face the winner of the last 32 clash between the Netherlands and Morocco.
"They're both good teams," said Broos of Canada's next opponents.
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"I think Canada have a chance because they play good football. They are powerful. There's speed in the team. So it's a rather modern team. And with the mentality that is in that team, they can can cause a surprise."
Broos, who led Cameroon to the 2017 Africa Cup of Nations title, said South Africa needed to adopt some of those Canadian virtues in order to prosper at international level.
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"Modern football is more than technique," the 74-year-old Belgian added.
"Modern football is power, speed. And when you don't have it in your team and you play against the team who has it, then it's difficult. And we had a difficult game certainly."
Big guns in action
Matches in the last 32 continue on Monday with three ties. Brazil take on Japan in Houston.
Real Madrid star Vinicius Junior scored four goals as Brazil topped a pool featuring Morocco, Scotland and Haiti.
Croatia outmuscle Ghana to take second place in Group L as England beat Panama
Japan finished runners-up behind the Netherlands in their group with one win and two draws.
"The team is united and that feeling is getting even stronger now," said Japan coach Hajime Moriyasu, whose side beat Brazil 3-2 at home in a friendly in October.
"We have a chance and it will be tough ... we will be at full force."
In the other ties, Germany face Paraguay at the Boston Stadium and the clash between the Netherlands and Morocco in Monterrey finishes off the day's proceedings.


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