The billionaire businessman emphasized, though, that he expects to secure the 1,237 delegates needed to win the party's nomination ahead of the Republican National Convention in July.
"I'm a closer," he said. "I get things closed."
Trump woke up Wednesday with 621 delegates.
He walloped Sen. Marco Rubio in the first-term senator’s home state of Florida on Tuesday, forcing Rubio from the race. He also won in Illinois and North Carolina, extending his lead over Sen. Ted Cruz of Texas as the once-unwieldy nominating contest narrowed to a three-person brawl with Ohio Gov. John Kasich, who won his home state's primary.
"I did well in Ohio, but I was running against a popular governor," Trump said Wednesday. He added: "I ran out of a little bit of time. I think if I had a day or two more, it would have been perhaps a little bit different."
Trump and Cruz are in a dead heat in Missouri, which was still too close to call on the morning after the Republican primary. The state has 52 Republican delegates.
"We started out with 17 people; we're down to three," Trump said on CNN. "But this has been a nasty one; I guess that's why your ratings are as high as they've ever been."
In a remarkable campaign fueled by anger, Trump has been under steady attack — by rival Republicans, by the Democratic candidates, by progressives, by super PACs determined to derail his candidacy, and by the president, who has twice taken shots at the GOP front-runner in recent days.
The tone and tenor of of the campaign will eventually shift away from divisiveness and Trump will make peace with the Republican Party, he suggested Wednesday.
"I think there's a natural healing process, once the battle is over, once the war is over," Trump said. "I've gotten along with people all my life; this is actually a little unusual.... I think it will happen again."
He added: "We have to win, and as we win, people will forget and they will feel better. That's the way life is. After we put it away, a lot of feelings will be soothed."
But, Trump said in a subsequent interview on MSNBC: "We don't want to lose the edge. We still have two people left."
Asked Wednesday whether he'd consider Rubio for vice president, Trump deflected the question, telling MSNBC: "It's just too early."
Trump noted that he liked Rubio — "until about three weeks ago, when he started getting nasty.... I was very surprised when he started doing his Don Rickles routine on me."
But, he said later on Fox News: "My whole life people have plotted against me, and I'm doing very well."
Speaking by telephone on "Fox & Friends," Trump said he plans to skip the channel's March 21 debate in Salt Lake City to deliver a previously scheduled speech at the American Israel Public Affairs Committee conference in Washington.
Trump told Fox that he'll be delivering "a major speech in front of a very important group of people that night; it was scheduled a while ago." He said he can't and won't reconsider that commitment.
The Fox News debate was announced this week, and Trump said Wednesday that it came as a surprise.
"I thought the last debate on CNN was the last debate," he said. "I think we've had enough debates. How many times can the same people ask you the same question?"
He added: "I don't mind the process of debating; it turned out that I do it well.... But I think we've had enough."
This post has been updated.