Asked about the peaceful proceedings, Ruto said that the situation has been improving since 2007, and the next election will be even better.
Amanpour later asked whether outgoing President Uhuru Kenyatta, who supported Odinga's election bid despite Ruto being his vice-president, had been in touch since the election.
"Unfortunately, President Kenyatta has not seen it fit to congratulate me," he said.
Amanpour later quizzed Ruto on human rights, particularly his previous comments that there was "no room" for homosexuality in Kenyan society.
Amanpour also pressed Ruto on his controversial promise to deport Chinese people from Kenya, but the President-elect argued that he had been taken out of context.