They twice held the lead in the second half only to be pegged back by the world champions, with a converted try from Malcolm Marx in the closing stages leaving South Africa agonisingly short at the final whistle.
This victory was the All Blacks' sixth straight over South Africa and was the second successive time the world's best team has gone 6-0 in the Rugby Championship.
Coetzee said he knew the areas that required further work: "We had them under pressure at times, but you can not give the ball away against New Zealand".
"The changes they've made among the forwards tells us they are looking to shore up their lineout and maybe they'll come at us a bit more physically", Read said.
Australia ended with 15 points after two wins, two draws and two defeats.
Coetzee feels that they are building variety in their play, with tactical kicking part of the plan against New Zealand.More news: TransCanada Cancels Energy East Oilsands Pipeline
'While we've played some rugby for 80 minutes and played really well, there's been other games where we've played for 60 and clocked off.
"Guys like Siya Kolisi, Malcom Marx and Eben Etzebeth are leading from the front and they were outstanding today".
He was instrumental on defence and with ball in hand and also won several penalties at the breakdown which got the Springboks out of trouble on countless occasions.
Crotty scored in the first half following a charge down, Ioane's breakaway intercept try came against the run of play, and McKenzie's score near the end was the result of a brilliant break from deep.
"While it's necessary for us to try and anticipate what they're going to bring to the match, it's more important for us to focus on what we're going to bring to the encounter".
"A performance like this must give us belief - the players will get confidence from this". "The year is not over, we still have four matches left and will continue to seek improvement in those".