Rev Alexander Love was speaking after Home Secretary Amber Rudd formally approved the extradition of his son Lauri Love to the US to face multiple cyber hacking charges.
Love is alleged to have stolen data from US agencies including the Federal Reserve, the US Army, the Department of Defence, Nasa and the FBI in a spate of online attacks in 2012 and 2013.
The 31-year-old has Asperger's Syndrome and also suffers from depression. Some have said he is not fit to stand trial in the US and should be tried in the UK instead.
He faces the possibility of three separate trials in different jurisdictions and faces 99 years in prison if found guilty.
There are 14 days to apply for permission to appeal against Amber Rudd's decision to extradite him.
Rev Alexander Love said: "It was going to happen - it was inevitable - but it's still painful. I cannot begin to express how much sorrow it causes me.
"All we are asking for is British justice for a British citizen."
Lauri Love has called the extradition decision an "aberration of justice" and has said he fears he will die in prison.
