Justice Michael Lee said the pair failed to inform the board of potential risks related to overseas junkets with alleged criminal connections and false claims about customer use of credit cards for gambling purposes.
The lawsuit - brought by the Australian Securities and Investments Commission - failed to prove however that Star's former chair John O'Neill and six board members also contravened the law.
In his 501-page judgment, Justice Lee dismissed the claims against these non-executive directors finding they would not have known of Mr Bekier and Ms Martin's missteps.
However, he criticised them for their "self-congratulatory" evidence presented at trial.
He noted the board had not actively pressed management, including Mr Bekier, about whether Star was being run ethically or lawfully.
"(Running a casino operator) was no ordinary enterprise, and the role demanded vigilance," he wrote.
Directors had to be more than passive receivers of information even if board packs they received were voluminous, the judge said.
While artificial intelligence could be used to navigate material provided by management in a controlled and transparent manner, board members should not become reliant on computer-generated output, he wrote.
"(A director) is expected to take a diligent and intelligent interest in the information available to them," the judge said.
"The use of technology may assist comprehension, but it cannot displace judgment."
A spokesperson for the Australian Institute of Company Directors said Thursday's decision gave important feedback around directors' duty of care and diligence.
"The decision provides some clarity on key questions including the role of the board versus management, the volume and quality of board papers and the need for active board oversight," he said.
"The clear message for boards is that active oversight of non‑financial risk must be a focus, and especially so in high-risk, highly regulated sectors."
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