"We let ourselves and New Zealand down."
Speaking to media afterwards, Shaw said despite the low response rate, the department's repair work since – including by using tax records, birth records and drivers' licence data to make up missing information – meant some information would actually be more accurate than in 2013.
He said for the purposes of electoral boundaries, health and education, the data more than met its legal requirements.
However, he admitted some other data sets would not be able to be used.
The response rate among Maori dropped from 88.5 per cent in 2013 to 68 per cent in 2018. Because there are no other Government agencies that fully track iwi affiliation, there won't be any official data on iwi numbers release from the census.
Other data sets would also not be viable - although which would not be clear until the release of the data began in September, Shaw said.
During her resignation on Tuesday, MacPherson told media the decision to quit had been her own.
But National Party statistics spokesman Jian Yang on Tuesday accused Shaw of using the Government Statistician as a scapegoat.
Shaw was full of praise for MacPherson's work in trying to repair the census, but when asked if he had called for her to quit, he repeatedly said it was "not appropriate" to discuss the matter.
He also declined to say when he had found out she was resigning.
"She's been working to remediate it for over a year now, so I'm sure her responsibilities have been weighing heavily on her shoulders that entire time," Shaw said.
Asked if she had made the decision entirely on her own, Shaw twice replied:
"She made the call to resign," adding: "I support her decision."
Shaw said he had asked the review to specifically look into whether Ministers could have done anything more to fix the situation, and had received no criticism back.
MacPherson will stay on until Christmas to oversee the clean-up effort and the Government will begin recruiting for a replacement in coming weeks.
Tuesday's report - carried out by professional director Murray Jack and former Canadian Census assistant chief statistician Connie Graziadei - found Stats NZ was slow to react as it became clear the results were not coming in as expected.
"It is in our view that the focus on online responses and overly optimistic view of 'Stay the course. The paper will come', led to insufficient action being taken at the appropriate time," they said.
It also said too much focus had been put into the online work with not enough testing or attention paid to the paper side of the process, and that the burden of the North Canterbury earthquake – which closed Statistics NZ's offices in November 2016 – was underestimated.
The report has made 16 recommendations, including that the next census still be held in 2023, saying 2021 would not leave enough time for a safe redesign.
MacPherson was first appointed in August 2013. She was reappointed after the Census in August last year with her term due to end in 2021, according to the State Services Commission.