Australia completed an innings and 52 run victory over McCullum's side about an hour after lunch on the fourth day on Monday.
The hosts were dismissed for 327 in their second innings, after being bundled out for 183 in their first, while the visitors scored a mammoth 562 with Adam Voges scoring 239.
"Australia were excellent right through from the moment they won the toss," McCullum told reporters. "From lunchtime on the first day we were trying to play catch up and were never able to do it.
"Conditions were difficult on that first morning. When you're presented with conditions like that you need a little bit of luck. If we could have got 250, 300 ideal, but 250 then we would have been in the game.
"In the end we were completely outplayed."
The wicket aided a superb Australian attack then dried out and browned off much faster than expected, McCullum said.
Australia's batsmen capitalised, none more so than Voges, who was bowled by Doug Bracewell for seven in the final over of the first day only for umpire Richard Illingworth to call a no ball. Television replays showed the ball was legal.
"Richard Illingworth would be pretty disappointed with it I'm guessing," McCullum said. "It is a bit of a shame but I have said all the way along that you have to take the rough with the smooth in this game and credit to Voges for making it count.
"The strength of character to overcome that non-dismissal that night then to go on to post a sizable total shows not only how good a player he is but how strong a player he is as well."
The decision provoked more anger from New Zealand fans, who were already feeling their team had been getting the short end of the stick in controversial decisions.
In the third test against Australia in Adelaide in November, third umpire Nigel Llong failed to give Nathan Lyon out despite 'Hot Spot' technology indicating he had hit the ball before being caught.
(Editing by Peter Rutherford)
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