In a statement, Dominic Raab said the Foreign Office believes Anne Sacoolas should return to the UK.
He added the "UK would have acted differently" after the US secretary of state refused an extradition request for the suspect charged with causing the death of the teenage motorcyclist by dangerous driving.
The 19-year-old’s parents Charlotte Charles and Tim Dunn were informed of Mike Pompeo’s decision to refuse the request in a phone call with their constituency MP, Andrea Leadsom, on Thursday.
Mr Raab added: "I called the US ambassador earlier to express the Government’s disappointment about this decision."
He continued: "We feel this amounts to a denial of justice, and we believe Anne Sacoolas should return to the UK."
Anne Sacoolas, the wife of a US intelligence official, claimed diplomatic immunity after the collision and was able to return to her home country, sparking an international controversy.
Despite last night's announcement from the US, Harry Dunn's family are adamant Sacoolas will come back to face justice.
Their family spokesperson, Radd Seiger, told ITV News: "We've known right from the start the American administration had no intention of sending her back voluntarily so the announcement last night was no surprise at all."
He added: "Last night's announcement makes no difference to us, Anne Sacoolas will be coming back, I just don't know when."
Mr Seiger also said the Foreign Office's statement has been the "strongest worded" one he has seen yet.
He thought the decision not to extradite Ms Sacoolas would have an impact to international relations between the UK and the US.
He said the Foreign Office has a range of options, before adding: "I imagine one of them might be not sending some people back that the American's want to be extradited look you know the simple fact here is that Donald Trump is taking a wrecking ball to international relations."
"It's not so much tit for tat at the heart of every extradition treaty is the concept of reciprocity you have to be careful what you wish for," he told ITV News.
The Home Office submitted an extradition request for Sacoolas earlier this month, after she was charged with causing the 19-year-old’s death by dangerous driving in December.
Mr Dunn died after his motorbike crashed into a car outside RAF Croughton in Northamptonshire on August 27 last year.
On Thursday night, Radd Seiger, a spokesperson for Mr Dunn's family said US Secretary of State Mike Pompeo has turned down the extradition request.
Previously the US Department for State has said it has always been their position Sacoolas had diplomatic immunity, stating that a request to extradite somebody with immunity would be an abuse.
It is alleged Sacoolas was driving on the wrong side of the road when the collision happened.
On Sunday, Northamptonshire Police Chief Constable Nick Adderley said there had been two further incidents of American staff from the base driving on the wrong side of the road since the death of Mr Dunn.
A video reported to Northamptonshire Police on Saturday, appears to show a car with what appears to be a registration number used on US government vehicles in the UK on the wrong side of the road near RAF Croughton.
- Footage of another vehicle which appears to be on the wrong side of the road near RAF Croughton
The base is used as a United States Air Force communications station and Mr Adderley has since said he will fund driver training there.
The Chief Con said all new arrivals at RAF Croughton would receive lessons on Highway Code awareness, UK road laws and protocols.