"We know we made the right decision before God. We certainly don't think we did anything wrong," said Mr McArthur, general manager of the family-run Ashers bakery.
"We have no regrets about what we have done. God calls us to be faithful Christians, not only when things are good but when people oppose us," he added.
The business was yesterday found to have unlawfully discriminated against a gay customer, Gareth Lee, by refusing to make a cake with a pro-gay marriage slogan. Mr Lee, who launched legal action against the bakery with the help of the Equality Commission, was awarded £500 damages.
After a three-day court hearing and seven weeks of deliberation, County Court Judge Isobel Brownlie delivered her judgment to a packed courtroom yesterday morning.
The DUP's Paul Givan, who is attempting to introduce a conscience clause into equality law in Northern Ireland, squeezed into the public gallery with former Health Minister Edwin Poots to listen to the ruling, which took one-and-a-half-hours to deliver.
Judge Brownlie told the court she accepted that the defendants had "genuine and deeply held" religious views, but said the business was not above the law.
"The defendants are not a religious organisation. They are conducting a business for profit and, notwithstanding their genuine religious beliefs, there are no exceptions available under (law) which apply to this case," she said.
Judge Brownlie added that the law in Northern Ireland prohibited Ashers from acting as they did.
She said limitations in law "on the manifestation of religious beliefs are necessary in a democratic society and are a proportionate means of achieving the legitimate aim, which is the protection of rights and freedoms".
Judge Brownlie said a religious belief cannot dictate what the law is.
"That is a matter for the Assembly," she added.
Before the judge delivered her verdict, Mr and Mrs McArthur said the case had been very stressful for their family. However, they looked relaxed and happy as they shared a quiet joke before the judge entered court.
They later shared a smile when the company was found guilty of deliberate discrimination.
A delighted Mr Lee left court with his lawyer Robin Allen QC and chief commissioner of the Equality Commission, Michael Wardlow.
Mr Lee, who is to donate the £500 damages to charity, declined to discuss the case. His lawyer said it was a "very difficult task being a pathfinder in a discrimination case".
"(Mr Lee) is very glad the case is now finished and the result vindicates the decision he made to seek the support of the Equality Commission," Mr Allen added. While Mr Lee chose to stay silent about the case, Mr McArthur, supported by his wife, confidently addressed the waiting media.
"We are extremely disappointed with the judgment. We said from the start that our issue was with the message on the cake, not with the customer.
"We have always been happy to serve any customers that come into our shops," said Mr McArthur.
He added: "The ruling suggests that all business owners will have to be willing to promote any cause or campaign, no matter how much they disagree with it. We certainly don't think we did anything wrong."
Mr McArthur said he was disappointed to have lost the case, but added that it had given his family "the opportunity to speak about our faith and our beliefs, and for that we give thanks to the Lord".
"Our faith is very important to us," he added. "It determines how we live, how we bring up our children and how we run our business, how we meet and probably engage with others in our society. We can't just leave it out when we go to work in the morning."
Despite his confident demeanour, he looked momentarily rattled when someone asked: "What would you say to those people who think of you as bigots?"
He hesitated slightly, then smiled and walked to a waiting car holding his wife's hand.