The Proteas have won only one global one-day title, the inaugural Champions Trophy in 1998, and the world's top-ranked team crumbled under pressure at The Oval in a straight shootout for a semi-final place.
"I can take us to win a World Cup, I believe," De Villiers told a news conference. "I'm a good captain and I can take this team forward.
"There's more than enough talent and we've just got to get it right when it matters most."
South Africa lost a 1999 World Cup semi-final against Australia when they needed one run to win from the last four balls and were eliminated in the group stage on home soil in 2003 after misunderstanding the Duckworth-Lewis scoring system.
The loss to India was another major disappointment because South Africa started well and moved smoothly to 116 for one after being put in to bat before three batsmen were run out and they were dismissed for 191 in the 45th over.
De Villiers, the world's top-ranked one-day batsman who scored only 20 runs in three innings in the tournament, is focused on the 2019 World Cup.
"Not a lot of people believe that but I think that (winning a tournament) is not that far away," the 33-year-old said.
"It is very difficult to sell it on this kind of performance but that is what I believe in. We are very close as a unit and we have just got to make it work when in matters the most."
South Africa coach Russell Domingo admitted the pressure on the side would continue to grow.
"There's always going be questions until we do get it right," he said. "The longer it takes to get over that the harder it will be."
India, who cruised to their target with 12 overs to spare, joined England and Bangladesh in the last four and will know their semi-final opponents after the final Group B game between Sri Lanka and Pakistan on Monday.
Their captain Virat Kohli played down the significance of South Africa's reputation for under-performing in big games.
"To me, their batsmen looked pretty confident," he said. "If you get two run-outs quickly, then the mindset totally changes.
"Getting their big hitters early was a bonus. We asked our bowlers to make them play difficult shots."
(Editing by Ed Osmond; Editing by Ken Ferris)
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