Goals from Junior Tchamadeu (34') and Christian Kofane sealed the result at the Agdal Medina Stadium on Sunday, with only substitute Evidence Makgopa (88') on target for South Africa late on.
Broos' side were looking to at least replicte their semi-final finish from the last AFCON, and made it through the group stages with wins over Angola and Zimbabwe and a loss to Egypt.
They then found themselves second-best to a make-shift Indomitable Lions side that was put together just a few weeks before the tournament.
Cameroon will now play hosts Morocco in the quarter-finals at Prince Moulay Abdellah Stadium in Rabat on Friday.
Reflecting on an unsuccessful AFCON, Broos explained in the Sowetan: "It's emotional, and there is frustration. And you know when emotions are high sometimes when you say certain things you regret them later, and I am not going to do that.
"In the coming days and weeks we will make a detailed evaluation of what was good and not good at this tournament. We will see what we have to change and what not to change because in six months there is the World Cup and we need to be ready for that.
"We need to look at what the problems and good things there were so we are ready again in March to play those pre-World Cup friendly matches and we are ready for the World Cup.
"We have to evaluate what happened and try to be better going forward. I can make declarations now, but when you lose a game like this and you are eliminated from the tournament, you are frustrated, sad and disappointed.
“Sometimes you say things that you regret afterwards but we are going to evaluate our performances and see what we can do going forward.”