They included Adam Ashley-Cooper knocking on the ball over the line in the first half, while prop Pek Cowan was denied his first test five-pointer after Rob Simmons was penalised for obstruction.
"There were a couple of really good opportunities which we didn't finish off," McKenzie said. "We got over the line a couple of times, it was frustrating not to get the points."
While it was McKenzie's first win as coach over either the Springboks or New Zealand, he lamented that his side handed South Africa the keys to their own jail cell numerous times.
"There were a couple of soft moments where we piggy-backed them out of their territory - we had them down there pinned and let them off the hook," McKenzie said.
"We did all right in the first half against the wind, but in the second half we managed to find different ways to turn the ball over and keep ourselves pinned down.
"We got an outcome today, which is great, but I like to be consistent so we need to win again next week."
McKenzie played down prop James Slipper's early exit from the field ahead of next week's clash against Argentina on the Gold Coast.
"That's just the perils of putting your head in the front row - he's all right, just a bit stiff."
Australia 24
South Africa 23
- AAP