Among the calls for help was for a person suffering a cardiac arrest, who died by the time their triple-zero call was returned.
The telco was fined $3 million on Wednesday for 473 breaches of its obligations as the national operator of the emergency service after an investigation by the Australian Communications and Media Authority.
Contingency plans were initiated when the outage struck in the early hours of March 1, with Telstra transferring triple-zero calls to a list of backup phone numbers.
But 127 calls were not transferred to emergency services because several numbers on the list were wrong.
Caller details were instead provided to the relevant service using emails and other phone calls.
Another 346 calls were successfully transferred, but lacked key location information.
The communications authority's consumer lead Samantha Yorke said it was concerning the issue was a result of Telstra neglecting to update its backup phone data for a critical public-safety service.
"It must have fail-safe systems and processes in place at all times," she said.
"In this circumstance its systems and contingency plans failed people in real need."
The telco apologised and had a strong record of compliance.
It also took immediate steps once the problem was identified and made considerable efforts to keep the public informed during the outage.
"These actions go a long way to restoring the community's trust in this critical service," Ms Yorke said.
Telstra appointed an independent consultant to conduct a review of the incident and updated its list of backup numbers.
A Telstra spokesman said the company let people down and acknowledged there had been unacceptable failures.
"We apologise wholeheartedly to everyone who was impacted when calling triple zero during the disruption," he said.
"We worked quickly to understand what occurred and made appropriate improvements so that everyone can be confident that triple zero will be there to support them when they need it."
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