KTRK-TV asked Cruz what was he thinking to kick off the sit-down interview; the senator replied he was simply trying to be a dad.
"I recognized that, yes, I have responsibilities as a dad, that's what I was trying to take care of, but I also have responsibility as a senator," Cruz said.
The high-profile Republican lawmaker said he and his family were among the many Texans who lost power. So his daughters came up with an idea.
"They said, 'Look, let's take a trip. Let's go with some of our friends and let's get out of here and let's go somewhere warm," Cruz recalled. "And [Cruz's wife Heidi] and I said...'OK.' And we did. So we booked a trip.'"
After his return to Houston on Thursday, he quickly admitted that he regrets the decision to plan the getaway with his family. He told KTRK he began feeling second thoughts the minute he sat down on the plane.
"As a leader, you need to be here. You need to be here when Texans were hurting. That's why I didn't feel good about it even as we were heading out," Cruz said.
WATCH: Ted Cruz 'regrets' decision to take Mexico getaway during crisis
"You question what I was thinking, I was trying to take care of my family. I was trying to take care of my kids," said Cruz. "It's unfortunate, the firestorm that came from it. It was not my intention in saying yes to my daughters to somehow diminish all the Texans that were going through real hardship."
KTRK asked Cruz how can he justify leaving, as many are outraged over his actions.
"In hindsight, if I understood how it would be received, the reaction people would have, obviously I wouldn't have done it. It was a mistake," Cruz said.
Cruz said one of the things he regrets is this incident being used as a distraction from the "real issues" such as, he said, why the state's electrical grid was unprepared. He agreed, however, it wouldn't have been a distraction if he remained home.
Cruz said a crisis is playing out in Texas, with back-to-back winter storms as well as "the disaster of people all across the state who have lost their power."
The senator recalled one woman on the plane who said it was "embarrassing" for the state of Texas not to have power.
"I got to say it's ridiculous," Cruz said.
"Texans want the power back on," he continued, "They want the water back on. They want the problem solved, and all of this is distracting from that problem."
Hundreds of thousands of people in Texas woke up Thursday to a fourth day without power, and a water crisis was unfolding after winter storms wreaked havoc on the state's power grid and utilities.
Texas officials ordered 7 million people - one-quarter of the population of the nation's second-largest state - to boil tap water before drinking the water, after days of record low temperatures that damaged infrastructure and froze pipes.
In Austin, some hospitals faced a loss in water pressure and in some cases, heat.
Cruz told KTRK there should be a thorough investigation into Texas' power grid, but doesn't think the federal government should take it over.
"It is maddening that Texas couldn't handle a few cold days. That is really frustrating and the fact the grid didn't operate is completely unacceptable, but I don't want it to become an excuse for the feds to come in and take over everything and drive up the cost of Texans every day of the year in perpetuity," Cruz said.
The senator said Texans have come together to deal with disasters many times in the past.
"It's never more inspiring than seeing how Texans unify in the face of hardship," Cruz said.
Cruz's office told ABC News the senator took a COVID-19 test Thursday morning to comply with mandates on traveling to the U.S.
Earlier in the day, a source familiar with the senator's travel schedule told ABC News Cruz was originally scheduled to return to Texas on Saturday with his family.
The Houston Police Department confirmed a member of the senator's staff contacted the department at Bush Intercontinental Airport on Wednesday to request assistance for Cruz's arrival the next day.
"Upon Senator Cruz's arrival at Terminal E, HPD officers monitored his movements through the terminal," said Houston Police Chief Art Acevedo.
Houston Police Department spokeswoman Jodi Silva could not say whether such requests are typical for Cruz's travel or whether his staff has made a similar request for his return flight.
U.S. Capitol Police officials and the Senate Sergeant-at-Arms have encouraged lawmakers and their staff to be conscious of potential threats and to consider advising law enforcement about their travel at airports and other transportation hubs.
The incident opens Cruz, a key ally of former President Donald Trump, to fierce bipartisan criticism in Texas and beyond as he contemplates the possibility of a second presidential run in 2024. The two-term senator's current term expires in early 2025.
"That's something that he has to answer to his constituents about," state Republican Party Chairman Allen West said when asked whether Cruz's travel was appropriate while Texans are without power and water.
"I'm here trying to take care of my family and look after my friends and others that are still without power," West said. "That's my focus."
KTRK asked Cruz if he would have returned home had it not been for the outrage on social media.
"As I said, I was having second thoughts even as I sat down on the plane. I flew down with my family last night. I talked to Heidi last night before we went bed and I said, 'I think I need to come back tomorrow. I need to be in Texas. It's not right for me to be here.'"
Cruz said his intention was to work remotely from Texas using email, phones, and Zoom.
"But even so, I needed to be here. It was a mistake not to (stay). So I changed my flight to come back today and it was the right decision to come back," Cruz said.
Cruz has been demonized by the left even before he ran for president in 2016. In more recent years, he has positioned himself as a Trump loyalist with an eye toward a potential second White House bid.
The Texas senator, who once described Trump as a "pathological liar," championed the-then president's call to block the certification last month of Democrat Joe Biden's election victory. That stand led to calls for Cruz's resignation after a violent mob stormed the Capitol as Congress was affirming Biden's win.
"Ted Cruz had already proven to be an enemy to our democracy by inciting an insurrection. Now, he is proving to be an enemy to our state by abandoning us in our greatest time of need," Texas Democratic Party Chair Gilberto Hinojosa said Thursday. "For the 21st time, the Texas Democratic Party calls on Ted Cruz to resign or be expelled from office."
Cruz's office dismissed calls for his resignation earlier in the month.
"The left - and some grifters on the right - are consumed by partisan anger and rage," his office said in a written statement. "Sen. Cruz will continue to work for 29 million Texans in the Senate."
In the interview, Cruz responded to those calling for his resignation in the fallout of his Cancun trip.
"Let's be very clear, the angry haters screaming resign...we're at a very divided place in our country where people are screaming vitriol and hate. I think that is a sad sign of where we are," Cruz said. "I don't do that to other people. You don't see me screaming at people I disagree with that they need to resign."
KTRK asked Cruz how does he earn back the respect of those who are upset over the "optics that he left instead of staying."
"Candidly, the press is obsessed with optics," Cruz said. "Many of the people who are upset with me were upset with me before we started. There are people on the far left who disagree with me politically. That's fine. You are allowed to disagree with someone politically. I wish that more of the angry left, more of the people who scream and yell and are filled with hatred, I wish they'd learn to just treat people with civility and respect."
The Associated Press contributed to this report.