Tillerson, who was fired in March, made no attempt to deny his poor relationship with Trump during a rare interview Thursday night as part of a charity dinner in his native Texas.
"I think part of it was obviously we are starkly different in our styles. We did not have a common value system," Tillerson told veteran journalist Bob Schieffer of CBS News, which broadcast an excerpt Friday.
"I'd have to say to him, 'Well, Mr President, I understand what you want to do, but you can't do it that way -- it violates the law, it violates a treaty.'
"He got really frustrated," he said. "I think he grew tired of me being the guy every day that told him you can't do that and let's talk about what we can do."
Tillerson, a former chief executive of oil giant ExxonMobil, had no government experience and had never met Trump when his nomination was promoted by Republican Party insiders, who hoped for a stable figure who could nonetheless appeal to the tycoon-turned-president with his outsider status and business background.
Tillerson immediately struggled to fit in, focusing on internal State Department streamlining rather than broader foreign policy goals as his relationship frayed with Trump.
"It was challenging for me coming from the disciplined, highly process-oriented ExxonMobil Corp to go to work for a man who is pretty undisciplined, doesn't like to read, doesn't read briefing reports, doesn't like to get into the details of a lot of things," Tillerson said.
Trump is proudly anti-intellectual, saying that he succeeds by following his instincts and knows better than experts.
Asked about his reading habits in an interview shortly after taking office, Trump said he was "looking at a book" but was distracted by phone calls every time he tried to get started.
Trump's most visible foreign policy actions include pulling out of international agreements including the Paris accord on climate change and a denuclearization deal with Iran.
Trump announced Tillerson's firing by tweet and, in a final indignity, the White House made it known that the nation's top diplomat was on the toilet when he learned the news.
He was replaced by Mike Pompeo, a brusque former congressman and CIA chief whose style appears more to Trump's liking.
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