Gregan, who became Australia's most capped captain in the match against South Africa, admitted the Wallabies had found it difficult to recover from the demoralising 13-9 defeat to the All Blacks in Brisbane.
"I think the boys were still flat on Wednesday, physically and emotionally," said Gregan. "You kind of know when the team is up and we were certainly down at training on Wednesday."
"We refreshed and recharged as much as we could between Wednesday and Saturday but it is a very good indicator to you if are travelling by Wednesday and we were still a bit flat.
"The boys had a go over the (New Zealand) match - a fair bit went into the match in Brisbane but that is the nature of the Tri Nations and back-to-back Tests, it is always tough to get over a big match for the next one, regardless of the result.
"The type of match we played last week was physically demanding, so it was a real mental challenge to get ourselves right."
Against South Africa, Australia squandered a 10-0 half-time lead to fall behind 18-13 midway through the second half.
But a late Mat Rogers try and a sideline conversion from centre Stirling Mortlock saw the Wallabies escape with a two-point win and keep them in contention for the 2006 Tri Nations series title.
However, with a less than impressive performance against the same team they trounced 49-0 in Brisbane three weeks ago, many questioned the Wallabies' composure in the face of pressure from the Springboks.
"I wouldn't say composure, I would say rhythm," countered Gregan.
"We struggled to get into the game with our attacking rhythm and we turned the ball over at times when on the attack in the first half.
"We made fundamental errors when we were building some pressure with the ball and that didn't allow us to play."
"But I think the pleasing aspect any time a team wins by a close margin is that they were able to show a lot of character in grinding it out and doing it for each other."