The All Blacks lost 19-14 to Australia on Saturday to give the Wallabies a 3-0 Bledisloe Cup clean sweep for the first time since 1929 and left them bottom of the Tri-Nations tournament.
Hart, visibly shaken at the loss, rejected suggestions that he would resign "if it was in the interests of New Zealand rugby".
He said: "I expect I'll get a lot of criticism. There's not much you can do about it. Mistakes were made and they were simple things that just went wrong. In the end I'm very committed to the job."
David Moffett, the New Zealand Rugby Football Union chief executive, stated before the match in Sydney that Hart would continue to have full support, whatever the result.
For the first time Hart attacked the All Blacks' performance and hinted that some players had slipped below acceptable standards. "We dropped ball we shouldn't have dropped, we threw bad passes. Those are things unfortunately you can't coach," he said.
Australian joy over their historic triumph has been marred by the prospect of Matt Burke, facing up to six months out with a shoulder injury. The full-back dislocated his right shoulder as he scored the decisive try.
Rob Macqueen, who took over late last year as Australian coach, said he was particularly pleased with the character of the team as they bounced back from defeat to South Africa last week.
"The attitude of the players from the day after losing to the Springboks was always positive and that makes a difference," he said.
"I don't think we could have come back from that if we didn't have a positive attitude. That's a great sign for the World Cup."
Australia: Try Burke; Conversion Eales; Penalties Burke 4. New Zealand: Try Cullen; Penalties Mehrtens 2; Drop goal Mehrtens.
AUSTRALIA: M Burke (D Smith, 73); B Tune, J Little, T Horan, J Roff; S Larkham, G Gregan; D Crowley, P Kearns, A Blades (G Panoho, 58), T Bowman, J Eales (capt), M Cockbain (O Finegan, 71); D Wilson, T Kefu (W Ofahengaue, 52).
NEW ZEALAND: C Cullen; J Wilson, E Clarke, M Mayerhofler, J Lomu; A Mehrtens (C Spencer, 68), J Marshall; C Hoeft (C Dowd, 70), A Oliver, K Meeuws, R Willis, R Brooke (I Jones, 51), T Randell (capt), J Kronfeld (S Robertson, 61), X Rush.
Referee: D McHugh (Ireland).