champions level with Australia and Pakistan on points, but a poor net run-rate ended their campaign.
India, who scored 152-6, needed to keep South Africa below 122 to go ahead of Pakistan's run-rate, but the Proteas rode on a 38-ball 65 from Faf du Plessis to make 151 all out.
Dhoni's men failed to make the semi-finals despite winning four of their five games, while the West Indies advanced with just one win without the use of the Super Over tie-breaker.
"I think it was quite a satisfactory performance," said Dhoni, who led India to victory in the inaugural World Twenty20 in South Africa in 2007 in his first stint as captain.
"In this tournament, we lost just one game, though we lost it badly," he said, referring to the nine-wicket loss to Australia in a rain-affected Super Eights match on September 28.
"We all know what impact rain has on bowlers, especially the spinners. So let us get practical about what the reason was and ask whether it was the real fault of the players.
"It is not, it can happen in this format. And when you are at a stage where other games involving other teams can affect you, you don't want that kind of situation."
Dhoni said restricting South Africa to less than 122 was never going to be easy in the second innings. His preference to bowl first and know the required target did not materialise after he lost the toss.
"It was a low score to defend," he said. "We won this game by one run, so it is difficult to say that if a few strategies had been changed, we could have defeated them big."
India have not made the semi-finals of the last three editions after winning the inaugural competition despite the huge exposure to T20 cricket in the Indian Premier League.
Dhoni, however, said playing in the franchise-based IPL did not count in the international arena.
"The IPL is very different," he said. "I have always said it is a domestic tournament. There are a lot of international players in all sides, but the role of the domestic players is very important.
"When you are playing against international sides, the bowling attack of the opposition is much better."
Dhoni and many of his team-mates will now travel to South Africa for another round of T20 cricket in the inter-club Champions League, an off-shoot of the IPL, which starts on October 9.
India will then host England for a four-Test series starting in mid-November.