"These managers have acknowledged their part in some of the things that went wrong and have chosen to resign.''
Mr Hughes said employment matters related to the Ministerial Inquiry have been resolved and the focus was firmly on moving forward.
He said the staff members had both made considerable contributions during their time at the ministry.
Last week Mr Hughes said he would investigate two senior staff members at the ministry.
On Tuesday the Minister Responsible for Novopay Steven Joyce confirmed Ms Jackson had been one of the two ministry staff who had been investigated.
Mr Joyce said after Ms Jackson's resignation that not all of the responsibility for Novopay failures could rest on her shoulders.
"A number of entities and people have fallen short of what's required, but I certainly respect the fact that she's decided that it's an appropriate course of action for her to take.''
Ms Jackson was the tertiary, international and system performance deputy secretary, and was formerly schooling deputy secretary.
"The report identifies shortcomings in areas for which I was responsible as deputy secretary, and was formerly schooling deputy secretary,'' she said on Tuesday.
She said the decision to resign was hers.
Ms Jackson was originally from England, and started at the ministry in 2005 as senior manager for tertiary education outcomes and strategy group.
She has also been general manager of the Centre for Social Research and Evaluation at the Ministry of Social Development, manager of strategic projects at the Education Review Office, and an education adviser with the Department of Prime Minister and Cabinet.
Both resignations followed a report on Novopay that found the Cabinet ministers who had signed off on Novopay received misleading information from officials.
The June 5, 2012 paper to ministers was sent by the ministry's chief information officer Leanne Gibson and recommended the project should proceed as planned, but said there were 147 defects which had not been solved.
Despite the two staff being in the firing line, a memo in April last year showed the ministry considered dumping the troubled payroll system.
The confidential memo, again from Ms Gibson, sent to Anne Jackson, gave detailed problems with the development of Novopay, and recommended options including terminating elements of provider Talent2`s contract and moving to a hybrid system incorporating Novopay and the previous Datacom system.
Ms Jackson's resignation follows that of former Secretary for Education Lesley Longstone as a result of a poor working relationship with Education Minister Hekia Parata.
