Eunice and Owen Johns, of Derby, say they are considering an appeal over the High Court verdict.
The Pentecostal Christians were barred from fostering by Derby county council in 2007 after they admitted they believe homosexuality is unacceptable.
They took their case to the High Court but Lord Justice Munby and Mr Justice Beeston ruled that their views could harm foster children.
“The equality provisions concerning sexual orientation should take precedence” over religious beliefs, the judges ruled.
They also dismissed the couple’s lawyer’s claims as “a travesty of reality”.
Speaking outside court, Mr and Mrs John said: “We are extremely distressed at what the judges have ruled today.
“All we wanted was to offer a loving home to a child in need. We have a good track record as foster parents.
“But because we are Christians, with mainstream Christian views on sexual ethics, we are apparently unsuitable as foster parents.
“We are unsure how we can continue the application process following the court’s ruling today.
“We have been excluded because we have moral opinions based on our faith and we feel sidelined because we are Christians with normal, mainstream, Christian views on sexual ethics.
“The judges have suggested that our views might harm children. We have been told by the Equality and Human Rights Commission that our moral views may ‘infect’ a child.
“We do not believe that this is so. We are prepared to love and accept any child. All we were not willing to do was to tell a small child that the practice of homosexuality was a good thing.
“Worst of all, a vulnerable child has now likely missed the chance of finding a safe and caring home at a time when there are so few people willing to foster or adopt.”
The couple added: “We have not received justice. We believe that an independent inquiry is needed to look into this.”
But gay and secular groups said the verdict was correct.
Naomi Phillips, of the British Humanist Association, said: “When we take on jobs of public service to others, particularly to vulnerable children, we need to understand that our own prejudices and preferences come second to the needs and rights of those we are helping.
“This judgment supports that principle and makes clear that this case has nothing to do with treating religious people unequally, or forcing anyone to go against their beliefs, or about religious discrimination, as was claimed in court.
Ben Summerskill, of gay rights charity Stonewall, said: ‘We’re delighted that the High Court’s landmark decision has favoured 21st-century decency above 19th-century prejudice. In any fostering case the interests of the 60,000 children in care should override the bias of any prospective parent.”
“Thankfully, Mr and Mrs Johns’s out-dated views aren’t just out of step with the majority of people in modern Britain, but those of many Christians too. If you wish to be involved in the delivery of a public service, you should be prepared to provide it fairly to anyone.”
The Johns are the latest in a series of Christian couples to unsuccessfully challenge equality legislation.
Last month, a couple who own a hotel in Cornwall were ordered to pay £3,600 to a gay couple they refused a double room to.
Peter and Hazelmary Bull, the owners of the Chymorvah Private Hotel, argued that their Christian beliefs meant they could not allow two men to share a bed.