They were roundly penalised at the scrum and breakdown in the first half, only to be let off the hook by poor goalkicking by Owen Farrell, while they were also guilty of kicking too much.
After a scintillating 54-16 win over Argentina in Rosario to turn their season around, and an admirable 41-33 to the All Blacks, it was a deflating display which dashed their grand slam hopes.
"It's massively disappointing,'' McKenzie said. "We thought we could win this game. I still think we could have won the game.
"We were competitive in some respects but, until the scoreboard is favourable, I'm not going to sit here and pretend anything other than it's a loss and the disappointment that goes with that.''
Form duo Israel Folau and Michael Hooper were again impressive, Cooper mixed good plays with indifferent ones and Matt Toomua barrelled Billy Twelvetrees for Australia's only try.
The loss of breakdown force Scott Fardy, in doubt for next week's clash with Italy, from a head clash on man-of-the-match Mike Brown was costly.
England coach Stuart Lancaster highlighted the state of the inconsistent Australian scrum when he freely said the English pack would face a much bigger challenge next week against Argentina.
Under-pressure lock James Horwill ripped in but another deposed leader Will Genia struggled badly with his kicking, highlighted by a charge-down by prop Mako Vunipola for Chris Robshaw's try.
McKenzie put Genia's poor kicking down to pressure.
"We didn't take the moments,'' he said.
"I thought we did pretty well first half - we fought a 7-1 penalty count against us at the 35-minute mark yet we led at halftime.
"There were bits for us to work with but we've got to keep our composure in the last play of the game.''
-AAP
