Michael Cheika issued an apology to Australia fans after England secured a historic Test series victory in Melbourne on Saturday.
The Wallabies needed a win at AAMI Park to keep the three-match series alive, but were beaten 23-7 by Eddie Jones' side.
A heroic defensive display from tourists earned them a maiden series victory Down Under with one match to come in Sydney next weekend.
The Grand Slam winners also replaced rivals Australia, who enjoyed plenty of possession but only had a converted try from captain Stephen Moore late in the first half to show for it, at number two in the world rankings.
Wallabies head coach Cheika said: "Obviously, we're very disappointed and we apologise to our fans.
"Honestly, we've had such great support and it's very disappointing to me - too many errors; too many dropped balls at key moments.
"[We] had plenty of opportunities to score, dropped the ball on several occasions close to the line and I don't think we trusted our skills in the key moments."
Skipper Moore is determined to salvage some pride and avoid a whitewash next weekend.
"We play for our people and our jersey, it's another opportunity to put the jersey on and show what it means to us," he said.
"[There is] Never a lack of motivation, every time it's special.
"Gutted about the series, but it's another opportunity to improve during the week and put that jersey on."