The Australians, who seized control of the Melbourne Test from lunch on the second day to wrap it up in the first over after lunch on the final day, take a 1-0 series lead to Sydney for the final Test starting Monday.
"I don't know what he was trying to achieve out of it, whether he was trying to get under our skin and unsettle us a bit," Ponting told a post-match press conference.
"But when you make big statements like he has, then it puts yourself under a bit more pressure. Every innings he has had, he's got off to a start but then got out," Ponting said.
Before the first Test, the South African captain said Ponting's team were "scared of losing in Australia" and that some of them were inexperienced in international cricket.
"I guess sitting here right now, we've had the last laugh," Ponting said.
Capitalising on a giant momentum shift from a record 107-run last wicket partnership in the first innings between man-of-the-match Mike Hussey (122) and Glenn McGrath (11), Australia dismissed the Proteas for 181 to claim a pyschological victory.
Ponting, whose captaincy had been questioned in the drawn first Perth Test, had few critics this time as he led the Australians and claimed a first innings 117 as well, in contrast to Smith's knocks of 22 and 25.
South African coach Mickey Arthur admitted Thursday that his team gave way under the pressure, and it was senior bowlers Shane Warne (4-74) and McGrath (3-44) who sealed the conclusive victory Friday.
"Mike Hussey and Glenn McGrath's partnership on day two has been the defining moment of the Test match," Ponting said. "Those extra 100 runs were vital for us."
He added: "We have dominated the last two matches and we are sitting here now 1-0 up, so that's a very good position for us."
Fast bowler Shaun Pollock remained 67 not out in the South African second innings and batted for 156 minutes, hitting eight boundaries and a six off Stuart MacGill.
Smith rued his team's missed opportunities. Andre Nel dropped Ponting on 17 before he went on to make 117, and Hussey was grassed by Jacques Kallis on 27 before he finished with 122.
"Our missed opportunities probably cost us the game," Smith said. "The middle of the game could have been so different. We could have had a lead.
"But their batsmen made the most of their opportunities, and credit to them.
"It took nine days of Test cricket for someone to really win a day. And that was yesterday, which Australia won.
"It's going to be a very tightly-fought series. We're 1-0 down and we're going to come back hard in Sydney."
There was controversy over the dismissal of No 5 batsman Ashwell Prince during Friday's first hour. After some vociferous appealing by Warne, Pakistani umpire Asad Rauf gave Prince out, caught at slip by Matthew Hayden for 26 after 147 minutes of resistance.
Prince was reluctant to leave the wicket, incredulous at the umpire's decision.
Television replays showed that Warne's sharply-turning legbreak appeared to deflect off Prince's upper arm, and not his bat or glove, before it went to Hayden.
Warne was criticised for excessive appealing to rookie official Rauf but match referee Chris Broad said that, although the leg-spinner had pushed the line, no action would be taken against him.
"There is a line and that line has been pushed, perhaps in this game, but according to the umpires they (Australia) haven't crossed it," Broad told reporters.
Warne, Test cricket's leading wicket-taker with 657, finished the 2005 calendar year with a record 96 wickets.
Australia have been unbeaten since their Ashes-series loss to England at Trent Bridge last August. Since then, Ponting's team have won five Tests and drawn two.
It was Australia's seventh win over South Africa in their last 10 Tests, with two drawn and the last loss coming in Durban in March 2002.