Wild added the parallel slalom title to the giant slalom gold he collected on Wednesday, a win that prompted criticism in the United States about his switch.
"No matter what you do in your life, people are going to hate you," Wild told a news conference.
"If you're good at something, people are going to hate you. It's just the way it is."
Wild said his decision had nothing to do with financial incentives.
"After the giant slalom there was a lot of questions: ‘How would you have done if you were riding for the United States, compared to riding for Russia?'" the 27-year-old said.
"I want everybody to understand - there was no question of, ‘If I continue riding for the United States, this is what I'm going to get, and if I start riding for Russia this is what I'm going to get'."
Wild said he had intended to quit snowboarding to go to college when the opportunity to represent Russia came up.
"I chose to continue snowboarding because I thought I could do something special," he said. "I thought I'd never reached my potential and I wanted to see how good I could get.
"That's why I continued snowboarding, and that's why I'm a Russian," said Wild, who became a Russian citizen after marrying Alena Zavarzina, the women's giant slalom bronze medallist in Sochi, in 2011.
Wild, who came from 1.12 seconds down to qualify for a final he won in spectacular style, praised the Russian team for the support they gave him in his quest for gold.
"I've got a tack, a guy who does my edges and does my wax, and there's no way I'd win today without him, no question," he said.
"I hurt my shin pretty bad the other week and the doctor for the hockey team was like 'hey man, let me help you.'
"People all over sports have helped me, so that's a big piece of how I was able to make it to the Olympics and ride well at the Olympics."
Earlier, Canadian snowboarder Michael Lambert told reporters that Wild had received hate mail calling him a "traitor" following his giant slalom victory on Wednesday.
Wild said there was nothing he could do about people expressing such sentiments.
"I think most reasonable people understand that it's just a guy who wants to do his sport and be the best that he can be," he said.
(Editing by Peter Rutherford)
