Owen and Bredge Ward, who were both 69, passed away in a hospital in Derry on Tuesday.
Last week, their family had hoped Mr and Mrs Ward, from Strabane, were recovering from Covid-19.
Instead, they are now preparing for their funeral on Wednesday.
Their son, Martin, said he was in “complete shock” and urged people to adhere to public health guidance.
Martin, who is one of six children, held his father’s hand as he died, while his siblings were with his mother at the funeral home.
He said his parents “doted” on their nine grandchildren and, sadly, they will never get to meet their 10th grandchild.
“We can’t do that because of Covid-19 and all the restrictions, which need to be in place.”
He said his mother’s condition started to improve last week, but then his father “went downhill” and was put into a coma.
“This is what the disease does – it can be mild or it can devastate lives,” he said.
“Within hours, my mum, who was improving, just went downhill. Maybe it was the shock.
“Fast forward a week and my father was improving and my mother was getting worse.
“She passed away yesterday, then my father, from a position where he was getting better, just completely collapsed and within a couple of hours of my mother dying, he passed away too.
“Even though they were sedated and had pain relief and loving care from the staff at Altnagelvin Hospital, both of them just completely collapsed within a couple of hours and that’s just how it is.
“It’s the hurt and suffering that this virus can cause.”
Martin, who lives in GalwaY with his young family, said Covid-19 guidance should be the same on both sides of the border.
“It’s a cross-border thing,” he said.
“We live on an island and we can’t separate each jurisdiction because it impacts upon all of us. It impacts on communities on both sides of the border.
“The only thing I want to say to people north and south of the border is to think about other people.
“We knew from February or March what could happen and people have to take on board that this can cause a hell of a lot of harm to people’s families.
“The economic aspect is terribly damaging too, so we have to try to limit the spread and adhere to the guidelines, social distancing where you can and when you can’t, put on a face mask.
“Treat everyone the same – with respect and as if they are one of your family – so you can minimise the harm to others.”
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