Captain Jean de Villiers scored two tries and Patrick Lambie added another in the final nine minutes at Newlands on Saturday, as South Africa earned a precious bonus point to crank up the pressure on leaders New Zealand.
Until that late blitz, the match had been a tightly contested affair, with Australia having lead 10-5 at the break.
McKenzie lamented his team's capitulation from that point, but he felt that the effort shown by his players had deserved a better outcome.
"To let in three tries at the end was a really disappointing finish and probably an unfair reflection on the contribution that the team had put in across that 70 minutes," the Wallabies coach said afterwards.
"I feel sorry for the players, they set the game up for the win and that won't be reflected in the final score, it will probably be forgotten.
"There was some really good stuff from our guys, we were in a good position to win it.
"We will have to look at the video and see why we didn't."
South Africa trail New Zealand by just one point at the top of the standings, but the All Blacks can wrap up the title by beating Argentina in Buenos Aries.