"Donald and his team, it's almost like they're subjects in a course in clinical psychology. The conduct they do, literally, they accuse others of doing," Cruz told moderator Anderson Cooper during the event, which took place in New York ahead of Tuesday's primary.
"What Donald doesn't like is losing elections," the Texas senator said.
Cruz also predicted Trump would have trouble getting the support of Republicans at a contested convention
"In Cleveland, I believe if it's a contested convention ... we're going to be in the much stronger position to earn the majority of delegates and earn the nomination of the party," Cruz said.
"In Wisconsin, the day before the election, Trump predicted a big victory," Cruz said. "What we saw was the party unify and come together, that's what its going to take to win the nomination."
The Texas senator also scoffed at Trump's accusations that the rules of the Republican nomination process are "stacked against" him
and the national party is rooting for him to lose.
"Anyone who knows anything about Washington knows the establishment is not rooting for me," Cruz said. "The rules are simple, the way you get elected is you win a majority of the delegates in the elections. I think the way you win is you make the case to the voters and you win their votes."
Rubio as veep?
Asked about considering former presidential rival Marco Rubio
for vice president, Cruz did not directly say he was looking at him, but refused to rule him out.
"He is someone that you would be a fool not to look at, he is very, very talented," Cruz said. "I think very highly of Marco, he is an amazing communicator."
Cruz credited Rubio's 2010 run for Senate with inspiring him to run in 2012.
He also praised Rubio's humor, recounting the time that he watched internet pornography with then-Justice Sandra Day O'Connor while he was clerking in the Supreme Court. Cruz wrote about the episode in one of his books and Rubio texted him his shock when reading it for the first time.
"'Holy cow! You watch porn? Our oppo researchers missed that!'" Cruz said Rubio texted him.
Cruz denied that he played any part in the scorched-earth tone of the Republican contest -- or the back-and-forth between him and Trump over their spouses.
Earlier in the campaign, Trump had promised to "spill the beans" on Heidi Cruz
, and retweeted an unflattering image of her.
"When you talk about disputes among the wives, listen, Melania is a beautiful woman, she appears to have been a wonderful mother to their kids," Cruz said. "I have never -- and would never -- say something remotely negative about Donald's family or kids."
"On my end there's no truce to be had because we shouldn't be engaging those attacks, we should be talking about substance," he added.
Earlier in the conversation, Cruz expressed doubt, however, that he could every truly ignore Trump's social media presence
-- and admitted he follows his rival on Twitter.
"You could sit alone in the wood in the middle of nowhere," he said, "and somehow still hear Donald's tweets."
Family on the road
Cruz was later joined onstage by his wife, Heidi. She said the decision for Cruz to run for president while raising two young daughters took a lot of thought, but called it "an incredible learning experience."
"We have given them a lot of choices and they wanted to come on the road with us, they wanted to be part of this. I think they understand that it is something bigger than our family," Heidi Cruz said.
"And they're really excited to be part of something that their dad is doing, that their parents are doing, and they know it's for others," she said. "We talked about that from the very beginning: Why would dad run for president, it was to make this country a better place for other kids as well. So they were really excited to see what that meant."
Caroline, 7, and Catherine, 5, joined their parents to talk birthday parties and their favorite things.
Caroline, who turns 8 on Thursday, said she was looking forward to their Build-a-Bear birthday party.
She also admitted, with some prodding from her mom, that her favorite state was New York -- and that she particularly likes the American Girl store. The girls also would like to invite pop star Taylor Swift to the White House, if their dad wins the presidency.
Ted Cruz talked a little about the differences between Caroline (who he said was "rascally," like him) and Catherine, who was quiet throughout her time on stage, sitting on her mom's lap.
He said that Catherine gives the best hugs, which he dubbed "marshmallow hugs."
Asked by Cooper if he was more a product of the Northeast or Texas, Cruz chose the Lone Star State.
"When I went off to Harvard Law School my dad jokingly referred to it as missionary work," Cruz said.
Cruz had completed his undergrad studies at Princeton University by then, becoming the first member of his family to attend an Ivy League school.
"To be admitted to Princeton was an extraordinary thing," he said. "It was a world, frankly, that I didn't know. When I arrived there it was a scary place. You had a lot of young people who were the children of CEOs and titans on Wall Street and people with fame and wealth and power."