"You know, they've kind of come to this party late. So you know, I appreciate their view, but I don't think I need to do any more at this point," Kasich told CNN in a phone interview Saturday.
Kasich said the answer to that question is in the hands of the Republican National Committee.
"Nobody has been clearer about their feelings toward him, or not many, as I have been. You have a Republican National Committee and they have to figure this out," said Kasich.
Earlier in the day, Kasich released a statement
announcing that he will not vote for Trump. The Ohio governor told CNN that he will definitely not vote for Hillary Clinton, and may just leave the top of the ballot blank.
Kasich, Trump's former rival for the GOP nomination, got a lot of criticism from fellow Republicans for refusing to attend this summer's Republican convention, even though it took place in Kasich's home state.
He clearly now feels vindicated, though he insists Trump's lewd comments caught on tape were just the straw that broke the camel's back.
"This is not just a matter of what has happened within the last 24 hours. This is a matter of what's happened over the course of frankly the last two years," said Kasich.
"There was always -- somehow maybe the guy will change -- there's been no change. It's gotten worse," he added.
Kasich said he isn't sure if this will be a wake-up call for Republican voters, who nominated Trump over him.
"Frankly, if the Republican Party does not understand that the 21st century is about the politics of people, the Republican Party will die," said Kasich, echoing the core themes of his presidential run.
"The truth as I'm out talking about these different issues that affect people, sometimes I'm not sure that my party hears it," Kasich lamented.
He also said he worries what this latest Trump incident does to America's image around the world.
"I think this damages the way that people look at us. Now is it permanent? I don't believe it's permanent, but it is damaging at this point in time. There are people around the world that are probably in disbelief that this is how a presidential campaign is run in America," said Kasich.
Before this latest bombshell, Trump was doing well in Ohio, where his populist anti-trade message resonates. Kasich, who was twice elected Ohio's governor, said he isn't sure what will happen now with Trump in the Buckeye state.
"Nobody has been able to predict any of these things but I've always believed that a divider doesn't win. So I can't tell you if people are going to somehow justify this -- I hope not. I hope not," he said.