Cain tells NBC's "Today" show the weekend test balloting was "not a protest vote."
Cain says his performance shows "the voice of the people is more powerful than the voice of the media."
He won roughly 37 percent of the vote, compared to 15 percent for Perry and 14 percent for former Massachusetts Gov. Mitt Romney.
Cain also says he doubts Perry's poor showing was the result of his uneven performance earlier in the week in the Orlando candidate debate.
Cain says the straw poll illustrates that "people are listening to the message and not just, with all due respect, to the media."