Melissa Hamilton, from Killygordon, Co Donegal, in the Republic of Ireland, died two weeks after she was diagnosed.
Letterkenny General Hospital has apologised to her family.
But Mrs Hamilton's husband Seamus said that and the settlement meant little as it "doesn't bring Melissa back".
Mr Hamilton had sued for damages for nervous shock over the wrongful death of his wife.
The hospital admitted liability in the case in May.
The settlement was reached on Friday, with 900,000 euro (£649,000) awarded for the future care of Mrs Hamilton's three children, who are aged 10, six and three.
Mrs Hamilton died in August 2011, just nine days after the birth of her third child.
She had first been referred to the breast clinic at Letterkenny General Hospital in February 2010, where she was informed that she had a benign cyst.
In June that year, she visited her GP again with a discharge from her breast.
She was referred to the breast clinic for a second time, and was diagnosed with mastitis.
Over a year later, in August 2011, Mrs Hamilton attended a locum GP and was again referred to the breast clinic, where she was diagnosed with invasive breast cancer.
In his first interview since the settlement, Mr Hamilton told BBC Radio Foyle what was important to him was "to clear Melissa's name".
"That figure could've been 20m euro, it wouldn't have mattered one iota," Mr Hamilton said.
"I'm hoping that I've proved the fact that Melissa did all she could.
"I'm hoping that will go some way to help me to move on and show this shouldn't happen."
Mr Hamilton said he wanted the settlement to mark a point from which he could move on with his life.
"I don't want to have to live the rest of my life in anger - it's not a healthy way to be.
"There are certain people in the hospital that if an apology came straight from them it would've meant a bit more.
"But it's only a piece of paper, it doesn't bring Melissa back.
He added that his wife's death should show others it is worth seeking a second opinion in cancer diagnoses.
In a letter read to the high court in Dublin on Friday, Sean Murphy, the general manager of Letterkenny General Hospital, apologised "unreservedly" to Mrs Hamilton's family because her cancer had not been diagnosed and treated at an earlier stage.
The husband of a woman who died of breast cancer after two chances to have the disease diagnosed were missed has said a settlement of 1.35m euro (£973,500) "means nothing to me".