Speaking at a press conference this afternoon, Ardern said she would not have been happy to have Turei in a Labour-Greens Cabinet.
"This is an incredibly sad set of circumstances, but I think Metiria has made the right decision."
Ardern said she did not speak to Turei directly, but her party conveyed to the Greens this morning that Turei would not have a place in Cabinet if she was Prime Minister.
Since becoming party leader on Tuesday, Ardern has refused to comment on the issue.
Even today, she would not specifically identify what Turei had done wrong to warrant being blocked from Cabinet.
She said Labour remained committed to the Memorandum of Understanding it had signed with the Greens.
Turei said her decision to rule out a ministerial role was partly a concession to the Labour Party, who had raised concerns about the ongoing welfare controversy.
The relationship came under pressure in the last week, especially after Turei made further admissions about her past last night.
She revealed that she was once registered to vote in an electorate she was not living in so she could vote for a friend, and that she was living with her mother while she was on welfare - though she claimed the two were financially independent.
Speaking to reporters today, she said she considered resigning but instead ruled herself out of a Cabinet position - a job she would have "loved".
"Change is coming but change always comes at a price, and today I have paid that price," she said.
She remained committed to co-leading the party despite the fact she will not be on the executive if in government, and said she believed she could still be effective.
"I will continue to stand for New Zealanders who are poor and who are treated with discrimination by the welfare system.
"This work is important. It is more important than one person."
Co-leader James Shaw said he did not ask for Turei to resign. Neither did anyone else in the caucus.
Turei insisted that New Zealanders could still trust her, saying had not set out to deceive the public but had simply forgotten that she had once enrolled in an electorate she did not live in. At the time, she did not know she was breaking the rules by enrolling in Mt Albert electorate while living in Mt Eden.
Answering questions about her failure to disclose extra flatmates while on welfare, she said she was "certainly not asking for anyone to agree with what I've done" but she did not regret the fraud.
"My story is the last of the tools I've got for this conversation," she said.
Asked whether there were any more skeletons in her closet, Turei said: "I have nothing more. This is it."
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Turei admitted last night she enrolled at a Mt Albert address where she did not live in 1993 so she could vote for a friend.
Enrolling to vote at an address you do not live at is an offence.
Turei also confirmed her mother was a flatmate for part of the period she claimed the benefit in the 1990s. She said they were financially independent at the time.
She revealed last month that she did not disclose to Work and Income in the 1990s that she had extra flatmates while she was a solo mother on the domestic purposes benefit. But she did not reveal then that one of them was her mother.
