Amid intense scrutiny on the company, Vicki Brady fronted a barrage of questions about the telco's network failure on Wednesday, caused by a critical software fault that halted train lines and timed out business transactions.
The national disruption forced Telstra to conduct 639 welfare checks on triple-zero users, with seven requiring assistance after initially failing to get through.
"We have let our customers and Australians down, and for that I am deeply sorry," she told reporters in Sydney, hours after touching down from overseas.
"When something goes wrong, we're committed to taking accountability ... and fixing issues as quickly as possible."
It is the third major national outage in less than a year for the $56 billion giant, which powers about 25 million Australian mobile services.
Chief financial officer Michael Ackland said the ASX-listed behemoth was not responsible for a death of an elderly woman in South Australia on Wednesday.
"We can see no record of calls from (the family's) numbers accessing Telstra's mobile network to call triple zero," he said.
No active outages were affecting the local area at the time, with the company detecting good signal strength.
Mr Ackland added "a related call" was successfully made to emergency services from another number, and was connected and transferred correctly.
The woman's death is being investigated by South Australian police.
SA Liberal Senator Kerrynne Liddle has linked the death to Telstra's outage.
South Australia Police said they repeatedly attempted to contact Senator Liddle for information regarding the report without success.
Telstra's head said she was promptly told of the outage while on a European vacation.
She conceded even senior Telstra team members were victims of the outage and resorted to Microsoft Teams to relay the message about how thousands of customers were affected.
The press conference has come after anger over Telstra's corporate leadership swelled, with former treasurer Wayne Swan saying executive bonuses needed to be reconsidered after the outage.
But Ms Brady held firm, deflecting calls for her to slash bonuses.
"We again have very clear processes and governance when it comes to bonuses and remuneration," she said.
In May, Telstra sacked more than 100 people and merged two of its biggest technology divisions in a restructure, but the CEO denied job cuts had affected quality control systems.
"What I've seen so far is our people and our processes worked as they should have," she said.
The outage was largely resolved by late Wednesday and a solution for a separate "secondary issue" that prevented some users making triple-zero calls was in place by Thursday afternoon.
The overwhelming majority of the 600-plus welfare checks conducted by Telstra took place with no adverse outcomes reported, Communications Minister Anika Wells said on Thursday night.
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