Optus chief executive Kelly Bayer Rosmarin confirmed the company would not be paying back customers for Wednesday’s service meltdown because most would get “less than $2” in compensation.

Communications Minister Michelle Rowland said it was reasonable that people wanted a refund and urged businesses to keep their receipts to show proof of economic losses.

“Australians expect providers to compensate them when things go wrong and I think that’s reasonable,” Ms Rowland told the ABC.

“There is a reasonable expectation from Australians that if they are done wrong, if there is an outage of this nature that causes them to suffer loss in some way – be that economic or otherwise – that corporations will do the right thing by them.

“I urge that in every case from corporate Australia, including this one.”

The federal government has launched an official inquiry into the shutdown over claims that Optus failed to communicate during one of the worst network outages in Australia’s history.

Announcing the post incident review, Ms Rowland said people were left “desperate” for information and criticised the company for not speaking out earlier.

“This is essential, considering that yesterday some 10 million Optus customers were affected by this mass outage and many millions on top of that, consumers and small businesses alike,” she said.

“I have tasked my department to undertake a review into this. Primarily this is about the lessons learnt and ensuring that the industry overall can make the improvements necessary to mitigate what has happened here from happening again.”

Hospitals, banks, and transport networks were brought to a standstill during the shutdown that Optus executives have blamed on a “technical network issue”.

Ms Bayer Rosmarin denied claims of poor communication during the 12-hour outage despite customers and the government urging the teleco for more information during most of Wednesday.

Ms Rowland said large providers like Optus and Telstra had a responsibility to ensure their services were working effectively and flagged an independent investigation from the industry watchdog.

“Clearly, there is great concern to ensure this doesn’t happen in future, but we always want to make sure people are our top priority, keeping them safe, so they have confidence in triple-0,” she said.

The government will begin drafting a terms of reference for a post-incident review that aims to determine how it can assist large telecommunications providers to “improve the post-outrage process.”

Industry watchdog the Australian Communications and Media Authority (ACMA) has also launched a probe into Optus’ compliance with the rules requiring that emergency calls are successfully carried from mobile carriers to Telstra.

The Greens have pushed to establish a senate inquiry into the situation amid concerns Optus management failed to be upfront with the public.

Greens communications spokeswoman Sarah Hanson-Young said the party would “push to get the answers that are needed” through an inquiry process and called the lack of transparency from the national provider a “disgrace”.