After finishing in fourth place during Tuesday's New Hampshire Republican primary, former Florida Gov. Jeb Bush is looking towards a longer-term strategy for the GOP nomination.

"I think the field will whittle down eventually," Bush said in an interview with "CBS This Morning" early Wednesday. "I'm a patient person. I wish it all happened overnight, that's kind of the obsession of the pundits want that to happen but it'll happen. And when it does, I'm the one candidate that has taken on Donald Trump that does not believe he's a conservative."

Of Trump, who won the first-in-the-nation primary by a double-digit landslide, Bush said that the businessman's nomination "would be a disaster for the Republican party."

Bush predicted that if the billionaire landed on the GOP ticket, it "would mean landslide defeats for a lot of really good people that are serving right now."

"He's been insulting me all the way through," Bush said of his long-simmering feud with the Republican front-runner. "That's one consistency he's had. He hasn't been so consistent on health care, on taxes, on spending, on the second amendment or anything else."

On Ohio Gov. John Kasich's second place finish, Bush said "I commend John Kasich for the campaign that he ran."

Bush also defended his own campaign strategy in his post-primary interview. When asked if the money he has spent on the trail so far has been worth it, he said that he has not been "coordinating with the super PAC that spent most of that money."

"People in New Hampshire, I think, you know, took a pause and said that at least -- not related to Donald Trump -- but for the other people that the 60 percent that voted, they wanted someone who had a proven leadership record," Bush said. "And I do."

"We ran a good campaign as well and look forward to taking it now to South Carolina," he added.