Kasich praised the women's bravery Monday during his State of the State address in Medina, Ohio, the (Cleveland) Plain Dealer reported.
"Just about every day I search for what the Lord wants me to do. Because I know life is short, and I know my purpose on this Earth, whether I'm the governor or I'm a has-been, is to bring about some healing," he said. "No one rescued them. They rescued themselves. First by staying strong. Then by sticking together,"
Kasich presented the three women with the 2014 Ohio Courage medals.
The three were kidnapped and held captive for a decade in the home of Ariel Anthony Castro. They eventually escaped his home and sought help. Castro was sentenced to life in prison plus 1,000 years after pleading guilty to more than 900 counts of imprisonment.
Castro killed himself in prison in September.