The high court remanded the California case to lower courts on the grounds that the individuals who defended the law in court lacked legal standing to do so.
Cordileone of San Francisco, chairman of the U.S. bishops' Subcommittee for the Promotion and Defense of Marriage, spoke to Catholic News Service in Rome the day the court handed down its two decisions.
He was there to receive his pallium from Pope Francis in a ceremony Saturday, the feast of Sts. Peter and Paul.
The pope will present palliums to archbishops named in the past year. The woolen stole signifies an archbishop's authority over the Christian community.
In addressing the court's refusal to rule on the merits of a challenge to California's Proposition 8, the voter-approved initiative barring same-sex marriage, Cordileone noted that 7 million voters in California voted for the proposition and "many of them invested a lot of hard work and a lot of time and lots and lots of money against seemingly insurmountable odds."
In response to the court's ruling that DOMA is unconstitutional under the Equal Protection Clause, Cordileone said the court "overturned a law that respects and enforces the principle that it's in the best interests of the child to be raised by their mother and their father."
He said the effect of the court's decision is to "undermine in the law the principle that children have a right to a mother and father."
He also noted that to have a "healthy vibrant society we need to reclaim a marriage culture."
The archbishop pointed out that he has said all along that no matter how the court ruled "our work remains unchanged. We need to catechize our people about marriage."
"Even if the court issued a ruling that we liked, we would still have a lot of work to do in helping our people understand what marriage really is, why marriage is important for the public good and why it's essentially an institution to support social justice, justice for the sake of children," he added.
Cordileone said marriage has the status it does in law because it has always been a child-centered institution. Redefining marriage, he said, turns it into an "adult-centered institution" where the government "doesn't have an interest in people's love lives" or in "how people work out their intimate relationships."