There are at least two different answers that could be given here. The two answers have one thing in common. They both have a faith in the genius of the person who gets rich.
While they were active in business, Rockefeller and Carnegie both believed at least to some degree in the idea of Social Darwinism. That is to say that they both believed in unfettered competition. They believed that such competition would lead to a situation in which the best businessmen triumphed and exercised power over the economy. This would make the economy as efficient as possible.
Later on, both men came to espouse a similar, but somewhat different philosophy. They both came to believe in what is now called the “Gospel of Wealth.” According to this idea, the rich were still the fittest and best people. In this philosophy, however, they were called to help those less fortunate than themselves. It was the duty of all rich people to use a good deal of their money to help others. What is important, though, is that they were supposed to use their talents and wisdom and spend their money in ways that would be helpful. They were not supposed to just give money to the poor or the government. They were the best, so they could do the best job of spending that money.
In both cases, these men believed that the way to make America better was to leave things to the rich and successful businessmen.