"Yes, we're going to compete here. We don't expect to win here," Kasich told CNN's Jamie Gangel.
Kasich drew 16% of the vote in the Granite State Tuesday night, enough to well outpace his other contenders in the "establishment lane," including Jeb Bush and Chris Christie, who ended his campaign on Wednesday
. But they all fell well short of Donald Trump, who dominated the field with 35% of the vote.
Kasich, however, said he is confident he will perform well across the South. And he also said he was confident he can compete against Trump for the nomination, but it will take time.
"Over time, I sure do. What do you think I'd be doing down here? I'd go home if I didn't think I could compete. Of course I think I can compete," Kasich said. "You've got to remember, in this 24-7 news cycle, the narrative changes like the flip -- one minute you're dead, the next minute you're alive, the next minute you're dead, the next minute you're alive."
Kasich seemed to bask in his strong showing in New Hampshire, striking an upbeat tone and noting that he has attracted much more interest in his bid.
"The money's coming now, everybody wants a seat at the table. Not everybody maybe, but my early reports are people who sat around and said 'You know, I like Kasich, he's smart, he's experienced, he'd be a great president, but he's at 1% in the polls. What am I going to do? I'm not going to help him,' " Kasich said. "Now, all of the sudden, they're like, 'How do I get a seat at the table?'"
He then took a subtle dig at former Florida Gov. Bush, albeit not by name.
"If you take a look at the person that says that, they spent, like, well over $100 million, something along that, and they got nothing. So I'm not worried about what the other folks say," Kasich said.
The Ohio governor said he plans to stick to the positive campaign message that has carried him for eight months. But he vowed to fight back if other candidates hit him. In the months leading up to Tuesday's primary, both Kasichs campaign and the super PAC supporting him unleashing a torrent of attack ads
against Trump in New Hampshire.
"I'm not just going to sit there and be a marshmallow or some kind of a pincushion where people just pound me," Kasich said. "Where I come from, the blue collar town that I come from, if you came in and beat our football team, we just broke all the windows on your bus. That's just a joke."