The president is "pretty undisciplined, doesn't like to read, doesn't read briefing reports", and tried to do things in a way that violated the law, Tillerson said Thursday at a dinner to benefit MD Anderson Cancer Center.
"Thank you to Rex Tillerson for his service!"
"It violates the law", he said at a rare public appearance in Houston.
In it, he described what he perceived as a hard working relationship with President Trump.
"I'd say here's what we can do", the former Exxon CEO said in a Houston speech.
Trump's tweet Friday followed a host of others addressing a wide range of topics, from the "fake news media" to Special Counsel Robert Mueller's investigation into allegations of Russian collusion in the 2016 election.
"He was dumb as a rock and I couldn't get rid of him fast enough", Trump said on Twitter. President, I understand what you want to do.
Tillerson also said Trump frequently asked him to do things that he had to explain were illegal or otherwise ill-advised. "It violates the law, it violates treaty.' He got really frustrated", Tillerson said.
Tillerson, who reportedly called Trump a "moron" after a discussion with the president about the country's nuclear arsenal, was sacked in March and replaced with Mike Pompeo.
Breaking with his former boss, Tillerson said that "there's no question" Russian Federation interfered with our elections in 2016, and that the Kremlin's goal is to "undermine our confidence and undermine the world's confidence in us".
After a news report that he had called Mr Trump a "moron", with an expletive as an adjective, at the end of a meeting at the Pentagon, Mr Tillerson refused to directly deny having said it.
"Now it is a whole new ballgame, great spirit at State!" he said.
He was replaced by Mike Pompeo, a brusque former congressman and Central Intelligence Agency chief whose style appears more to Trump's liking.
When Trump selected Tillerson to serve as the 69th secretary of state, he praised him lavishly, saying: "His tenacity, broad experience and deep understanding of geopolitics make him an excellent choice for Secretary of State".
It's this back-and-forth that Tillerson thinks cost him his job.
Tillerson stepped down as Secretary of State in March.
Donald Trump allows no bit of criticism to go unanswered, Exhibit Eleventy-Billion.