Ms Fentiman made the comments about Shaun Drummond quitting as she announced the return of a former Queensland Health boss as his temporary replacement.
Premier Annastacia Palaszczuk announced on Wednesday that Mr Drummond had resigned, about the same time as Ms Fentiman separately told reporters she had confidence in the bureaucrat following criticism of a department proposal viewed as penalising whistleblowers.
Ms Fentiman said she was told earlier in the week Mr Drummond was stepping down and it was "entirely appropriate" the premier made the announcement because directors-general resigned directly to her.
The premier was responding honestly to a question at a news conference, the minister said.
"The timing of the announcement took me a little by surprise but at the end of the day it's the premier's call to make that announcement," she told reporters on Thursday.
"I was made aware he would be stepping down."
In a note to staff, Mr Drummond said his departure "has been a matter I have been considering for the last few weeks".
He also said he supported the minister's plan, "which is right for Queensland and right for the health system".
Ms Fentiman denied reports tensions between them led to his decision to leave, saying they had a "very respectful working relationship".
Mr Drummond finishes on July 23, only nine months after being appointed director-general under previous health minister Yvette D'Ath.
Ms Fentiman replaced Ms D'Ath in a May reshuffle amid criticism of the government's handling of issues such as maternity service gaps, bed shortages and ambulance wait times.
Mr Drummond came under fire in recent days after a Queensland Health submission to a review of public disclosure laws was made public.
The submission proposed criminal penalties against staff who disclosed inappropriate information to journalists.
"Consideration could be given ... to include penalties for inappropriately disclosing relevant information to journalists where a department is dealing with the matter," the submission said.
The proposal sparked concern among media, whistleblowers and the Australian Medical Association that those who exposed problems in the health system could be penalised.
It was quickly ruled out by Ms Fentiman.
Mr Drummond later said in a letter to the Courier Mail the suggestion was from the department and not him, and said the submission was "not calling for penalties for those who disclose information to journalists".
His replacement, Michael Walsh, was director-general from 2015 to 2019 and returns as the government searches for a permanent successor.
Ms Fentiman said Mr Walsh was an incredibly experienced public servant who knew the health system well.
"I am looking forward to working with Mr Walsh and I have the utmost confidence in his abilities," she said in a statement.
Opposition Leader David Crisafulli said the conflicting statements were another sign of chaos while the state faced a health system crisis.
"If government's reached the point that a premier and a minister won't even talk to each other in the middle of a crisis, how on earth is it ever going to be fixed?" he said.
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