The host nation were outplayed in the first half by Cape Verde, who were playing in the tournament for the first time.
South Africa's head coach told BBC Sport: "Not too many of my players came to the party in the first half, which was a total waste of time. We weren't much better in the second.
"Too many balls were played over the top at 100 miles per hour, which is something we don't want to do. Some of the players seemed to freeze when the whistle blew and lost their nerve. Perhaps for some of them the occasion was a bit too big.
"We now have to go for it in our next two games against Angola and Morocco. Of course we wanted to win and get a goal and get all three points, and we are not doomed yet. But we need to improve."
South Africa face Angola on Wednesday.