"I'm proud we put in, but not proud of our performance," Jones told the Sydney Sun-Herald newspaper after the match.
"We put ourselves in a position to win, but couldn't go through with it.
"There were some good things, but it wasn't consistently good enough.
"I still don't take much solace from the game."
But, after a good night's sleep and a chance to reflect on the good things, Jones was more upbeat on Sunday and keen to look ahead to the four-Test spring tour of Europe in November.
"I was pleased with the way we fought our way back into the game but it was still disappointing not to keep the pressure on," he said.
Jones said several aspects of the Test pleased him, including the performances of fly-half Mat Rogers, back-rowers George Smith and Phil Waugh, and rookie centre Lloyd Johansson, who scored a try with his second touch in international Test rugby.
"I thought George Smith was outstanding at No.8," Jones said.
"The balance was good with George and Phil Waugh at the back of the scrum.
"What we need now is a big jumping, running No.6 to complement them.
"I will be having an even closer look at Rocky (Elsom) and John Roe (for that position)."
Jones said he was impressed with Victoria-raised Johnansson when he came off the bench in the second half for his run-on debut.
"He's a good young player who, if he works hard, can become a good Test player," he said.
But it was former rugby league international Rogers who caught the eye with an outstanding display of running rugby despite the pressure of wearing the no.10 jersey for the first time at Test level.
While delighted with Rogers' showing, Jones was less forthcoming about the future of incumbent skipper George Gregan.
The veteran scrum-half, who equalled England prop Jason Leonard's world record of 114 Test caps against New Zealand, has found his future to be the subject of much speculation, and Jones was non-committal.
"I will have a chat with George in the next week or so," he said.
The spring tour is looming and is an ideal chance for Wallaby hopefuls to secure a place in the squad for the 2007 World Cup in France.
Australia will play four Tests - against France, England, Wales and Ireland - and Jones said the huge injury toll the Wallabies had suffered during this southern hemisphere winter had thrust young, inexperienced players into the spotlight.
"We have handed out 10 new Test caps this season - the most for a Wallaby team since 1996," he said.
"It has been one of the most challenging seasons on record (for the Wallabies) with four Tests against South Africa and two against New Zealand.
"But it has also been good to see a lot of players in circumstances that they might not have been in at this point (in their careers).
"It has certainly tested where they are up to.
"And the spring tour will give them the opportunity to cement their places in the Wallaby squad."