Mr Richardson said he felt he was "surplus to requirements" because of the way the commission was being run.
"Probably there wasn't enough discussion right at the beginning about the precise way things would work, and ultimately I came to a (view) that I was surplus to requirements," he told ABC Radio National on Thursday morning.
"The interim report that will now be done by the royal commission will be a very different document to the one that I would have done when I was doing the review, prior to the royal commission being announced."
Commissioner Virginia Bell announced Mr Richardson's sudden departure on Wednesday night, as her inquiry prepares for its initial report by the end of April.
Mr Richardson was originally recruited to produce an independent report into any potential intelligence failures leading up to the Bondi Beach terrorist attack, in which 15 people were killed when a father and son opened fire on a Hanukkah celebration on December 14.
But when Prime Minister Anthony Albanese announced a royal commission into anti-Semitism following the attack, Mr Richardson's work was folded into the broader probe.
On Thursday, the former spy boss turned US ambassador said his salary was also an issue.
"Quite frankly, what I was being paid wasn't consistent with the work I was doing," he said.
Mr Richardson declined to elaborate when pressed, only saying most people would understand.
He later clarified that he believed he "was being way overpaid" for his limited work.
The Australian Financial Review reported earlier in March that the former ASIO chief would be paid $5500 a day for his work as special advisor to the royal commission.
Treasurer Jim Chalmers said he was sad to learn Mr Richardson had quit the probe but hadn't spoken to him about it.
"I think the world of Dennis Richardson," he told ABC TV on Thursday morning.
"He is a person of such immense experience and knowledge, and hopefully we've been able to tap some of that before this development."
In a statement, Attorney-General Michelle Rowland thanked Mr Richardson for his work and said the commission would deliver its interim report by April 30, as scheduled.
Shadow Attorney-General Michaelia Cash said the former intelligence boss was a central part of the probe and suggested his resignation could seriously undermine the investigation.
Mr Albanese's government initially refused to call a royal commission into the Bondi massacre, instead tapping Mr Richardson to head a review of the adequacy of intelligence and law enforcement agencies before the attack.
Following weeks of political pressure, Mr Albanese relented and announced a broader inquiry to be headed by Ms Bell, a former High Court judge, to investigate anti-Semitism as well as any failures in the nation's intelligence services.
In announcing Mr Richardson's resignation in a statement, Ms Bell said he was uniquely well-placed to report on intelligence and security agencies' preparedness for a terror attack.
"Thanks to Mr Richardson and the senior members of his team... work on the interim report is well advanced," she said.
Ms Bell thanked Mr Richardson "for the valuable contribution he has made to the commission".
