The women, who cannot be named, were suing Robert Armellin for more than 400,000 Australian dollar (388,000 US) to cover the cost of raising one of the girls to the age of 21, Australian Associated Press (AAP) reported.
The birth mother of the twins, now aged four, had told the Supreme Court in Canberra that Armellin implanted two embryos even though she told him before the in vitro fertilisation (IVF) procedure in November 2003 that she wanted just one.
The woman said she had lost her capacity to love and her relationship had suffered as she and her partner were distracted by the everyday chores involved in raising twins.
The couple were seeking 398,000 dollars to cover the cost of raising one child, including private school fees, about 15,000 dollars to compensate for time off work, and an additional amount for medical expenses, AAP said.
The doctor's lawyer said the loss of freedom was common to all parents and argued the mother told him she wanted one baby only minutes before the procedure after previously consenting to having two embryos implanted.
The couple's solicitor Thena Kyprianou said her clients were shocked by the court's decision to dismiss the case and would consider an appeal, AAP said.
She said publicity surrounding the case had destroyed her clients' privacy.
The pair were widely condemned when the lawsuit was launched in September last year, prompting them to issue a public statement saying their issue was with their doctor's conduct, not the children that resulted from it.
"This has never been a case about whether our children are loved," they said in a handwritten statement. "They are cherished."
IVF involves fertilising an egg outside the woman's body before transferring the embryo to the womb.