NAB has admitted it is still failing to properly address all customer complaints despite its public commitment to lift standards amid the fallout of the banking royal commission hearings.

The admission comes as part of NAB's response to the Australian Prudential Regulation Authority's request for the bank to conduct an internal review following the regulator's damning inquiry into rival Commonwealth Bank.

NAB chairman Ken Henry, who was grilled at the royal commission this week, wrote in the report that NAB had discovered it had some of the same failings for which APRA had lambasted CBA - as well as others.

Dr Henry said NAB had been reluctant to set exacting standards for itself, and had not moved quickly enough to address weaknesses.

"Too often the voice of the customer has been missing from our decision-making," Dr Henry wrote in his foreword to NAB's self-assessment on governance, accountability and culture.

"And too often we have been prepared to accept good intentions rather than hold ourselves to account for operating with the required degree of urgency, consistency and discipline."

APRA this year slammed CBA as complacent and blind to threats in its business so long as profits rolled in.

The regulator found cultural issues at CBA including "a widespread sense of complacency, a reactive stance in dealing with risks, being insular and not learning from experiences and mistakes".

APRA subsequently asked other major banks to look at whether the same criticisms could be applied to them.

NAB's self-assessment admitted it had a poor record when it came to listening to and learning from customer complaints.

"Customers continue to report that NAB's complaints handling process is slow," the report said.

"NAB has not always been quick to recognise recurring patterns and deal with them diligently (and) ... persistent issues exist."