Australia led the All Blacks with two-minutes remaining in Dunedin.
The All Blacks coach was full of compliments on arrival in Brisbane.
The Canterbury first five-eighth will travel with the All Blacks for Saturday night's Test.
Despite the loss, Coetzee said they proved they were on an upward path and growing as the season progressed.
But victory came at a cost, with two players leaving the field injured.
The All Blacks have won their last five matches against the Springboks.
All four of the squad rested against Argentina will reclaim their starting spots.
Allister Coetzee is confident his side have released the demons of a 57-point thrashing.
Match play-by-play and highlights as the All Blacks beat the Pumas in Argentina.
Their second straight draw between Australia and South Africa means NZ lock up the title for 2017.
The All Blacks are without a number of key players for the match.