Chasing a competitive 304 for a win, Amla stroked 129 from 115 balls, which included nine fours and two sixes as the visitors reached the target off the last ball of their innings.
Amla reached his second hundred from 94 balls, when he guided a delivery from West Indies captain Chris Gayle [ Images ] to third man for three in the 30th over.
"It was a great effort from us to chase over 300 runs, and we have to look at the positives from this performance," said Smith.
"Hashim's knock was an incredible innings, and the rest of the guys batted around him very, very well. But I think he must take the credit for a great run chase.
"We would have loved to have finished the game more comfortably in the last over, and maybe we got a bit conservative there in the end. But we successfully chased over 300 on a second game pitch, and we are happy," he added.
When Amla was dismissed, South Africa needed 80 from 76 balls, and J P Duminy joined AB de Villiers [ Images ] to carry them the rest of the way in an unbroken stand of 80 for the fourth wicket.
In a dramatic finish, the Proteas needed one run from the last delivery, following a sensational final over from Dwayne Bravo [ Images ] in which he conceded a single to De Villiers off the first ball, a leg bye to Duminy from the next, and then bowled three dot-balls.
De Villiers however, formalised the result, when he swung the final delivery through mid-wicket, where Darren Sammy fumbled it, and then missed a throw at the bowler's end, as the batsman scrambled to make his ground.
The victory handed the Proteas a 4-0 lead in the five-match series.
Gayle was obviously, very disappointed by the result, although it came down to the very last ball of the match.
"Credit must go to Bravo for the way he bowled the final over," he said.
"But to get 300 runs, and lose was not good. We should have scored at least 30 or 40 more runs based on the start that Dale [Richards] and I gave the team, but we were very disappointing in the middle overs again, too many dot balls.
"But South Africa are in good batting form right now, and they took the game away from us. We also missed a few catches, and this is the inconsistency. At times, we do well with the bat, and then turn up and do something completely different with the ball.
"I am very disappointed, and feel heartbroken for our fans, who turned up in their numbers for this match," he added.
West Indies Innings:
Dale Richards c Smith b Tsotsobe 59
Chris Gayle c Duminy b Morkel 29
Shivnarine Chanderpaul [ Images ] c Tsotsobe b McLaren [ Images ] 66
Dwayne Bravo b Tsotsobe 46
Darren Bravo not out 45
Kieron Pollard b Langeveldt 26
Darren Sammy b Langeveldt 0
David Bernard not out 13
Extras: (b-1, lb-8, w-10) 19
Total: (for 6 wickets, 50 overs) 303
Fall of wickets: 1-64, 2-115, 3-191, 4-223, 5-282, 6-282.
Bowling: Charl Langeveldt 8-0-59-2, Lonwabo Tsotsobe 8-0-48-2, Morne Morkel [ Images ] 8-0-56-1, Ryan McLaren 10-1-45-1, Jacques Kallis [ Images ] 5-1-27-0, Johan Botha [ Images ] 10-0-50-0, JP Duminy [ Images ] 1-0-9-0.
South Africa Innings:
Graeme Smith [ Images ] b Dwayne Bravo 23
Hashim Amla c Bernard b Pollard 129
Jacques Kallis c Dowlin b Gayle 51
AB de Villiers not out 57
JP Duminy not out 32
Extras: (lb-6, w-6) 12
Total: (for 3 wickets, 50 overs) 304
Fall of wickets: 1-59, 2-178, 3-224
Bowling: David Bernard 4-0-25-0, Ravi Rampaul 9-0-58-0, Dwayne Bravo 7-0-41-1, Darren Sammy 7-0-34-0, Sulieman Benn 4-0-22-0, Chris Gayle 10-0-60-1, Kieron Pollard 9-0-58-1.