Narev said the bank had damaged stakeholders' trust.
"At the heart of the relationship of the Commonwealth bank and all its stakeholders lies trust - we can never take that for granted and we have a lot of work that we have to do - and that we are going to do," he said.
"Certainly, it is my priority in my remaining time as chief executive to really restore that trust."
Narev announced in August he will step down from his role by the end of June, following the bank's decision to "deal with speculation" over his position during the AUSTRAC allegations.
On Friday, the outgoing chief executive didn't hint whether the bank has settled on a successor, but guaranteed "the next will be better than the current one".
He also said the Australian economy was travelling "okay" with recent data showing a decline in the unemployment rate and an improvement in underemployment.
But Narev said, while figures show "generally an okay period of growth", household confidence remains low.
"Despite the economic data looking solid we overlay it with the sense that households are not feeling as confident," Narev said.
"What we really need to see in terms of a national policy debate is policy settings that give businesses a sense of stability predictability to invest, create jobs and create demand for labour which in turn ... makes households feel better off."