"I think the big thing is [voters] are seeing a lot of fight," he told ABC News' George Stephanopoulos, adding that his double-digit victory in Michigan was a "monster win."
Trump also said he would change his style, which many have called bombastic and crass, after the primaries.
"I think they’re going to see a very different person when this is all over with," he said. "I was hit very hard by Marco [Rubio], and I had to hit him back harder."
Trump also won the Hawaii caucuses, while Sen. Ted Cruz scored a victory in Idaho.
"We’re going to win in Ohio," he said. "That’s going to be a whole new ball game."
Kasich, who has yet to win a state, had the support of four in 10 late-deciding voters in Michigan.
"For the first time, people are starting to hear what I have to say," he said. "We’ll competing all across the Midwest. We’re still standing."
Republicans in Ohio and Florida will cast their votes for the candidates next Tuesday. But a CNN/ORC poll released this morning shows Trump maintaining a slight lead over Kasich in Ohio and a substantial lead over Rubio in Florida.