Following the ruling, Dominic Raab, the Foreign Secretary, said: “My thoughts today are with Harry’s family.
"While this judgment makes clear the Foreign Office acted properly and lawfully throughout, I appreciate that won’t provide any solace to the family in their search for justice.
"We stand with them, we’re clear that Anne Sacoolas needs to face justice in the UK, and we will support the family with their legal claim in the US.”
Mrs Charles and Mr Dunn's case centred on a 1995 agreement between the UK and the US, granting immunity to administrative and technical staff at RAF Croughton, which the US waived in relation to "acts performed outside the course of their duties".
At a hearing earlier this month, their lawyers said the Foreign Office "took upon itself the authority to resolve the question of immunity and ultimately and unlawfully decided to accept the US embassy's decision that Anne Sacoolas had immunity".
Sam Wordsworth QC told the court that Sacoolas had "no duties at all" at the base and therefore "never had any relevant immunity for the US to waive".
But Lord Justice Flaux and Mr Justice Saini found Sacoolas had diplomatic immunity "on arrival in the UK" under the Vienna Convention on Diplomatic Relations (VCDR) which had not been "expressly waived", meaning she "had immunity at the time of Harry's death".
The judges said: "We do not come (to) this conclusion with any enthusiasm for the result, but it is compelled by the operation of the VCDR."
Speaking after the ruling, Harry's mother Charlotte Charles said it was "disappointing" the court did not rule in their favour.
"The Government and Mrs Sacoolas need to understand that this court ruling is just a blip along the way," she told reporters.
"I promised my boy I would get him justice and that is just what we are going to do. No one is going to stand in our way."
His father Tim Dunn added: "I still wake up every morning in absolute disbelief that we are in this situation at all.
"It's bad enough feeling the horrible pain of not having Harry around and missing him, but I can't believe the governments are putting us through this.
"It all seems so cruel and needless and I am just as angry today as I ever have been but so determined to see it all through until we have justice."
Harry Dunn's parents are to appeal a high court ruling that their son's killer had diplomatic immunity, as it emerged they have struck a £5,000 costs cap deal with the Foreign Office.
The High Court judges announced on Tuesday that they accepted the Foreign Office’s claim that the US suspect Anne Sacoolas “enjoyed immunity from UK criminal jurisdiction."
Within hours, the family announced they would be taking the case to the court of appeal - and it is understood they are prepared to go up to the supreme court in their efforts to secure justice for their son.
They have a cost capping agreement with the Foreign Office whereby they will not pay more than £5,000 of costs if they lose, while the Government will pay them no more than £30,000 if their case fails.
Mr Dunn, 19, was killed when his motorbike crashed into a car being driven on the wrong side of the road by Ms Sacoolas outside RAF Croughton in Northamptonshire on August 27 last year.
Sacoolas, whose husband, Jonathan Sacoolas, worked as a technical assistant at the base, left the country a few weeks later after the US said she was entitled to diplomatic immunity.
The 43-year-old was ultimately charged last December with causing death by dangerous driving, but an extradition request was rejected by the US State Department in January - a decision it later described as "final".
Speaking about the family's next steps, Mr Dunn's mother, Charlotte Charles, said she hoped the President-elect Joe Biden would shift the state’s position and "show us that the US have morals".
Mrs Charles, and Mr Dunn's father, Tim Dunn, claimed the Foreign Office wrongly decided that Sacoolas had diplomatic immunity and unlawfully obstructed Northamptonshire Police's investigation into their son's death by keeping the force "in the dark".
But, in a High Court judgment delivered on Tuesday, Lord Justice Flaux and Mr Justice Saini said: "Our conclusion is that Mrs Sacoolas enjoyed immunity from UK criminal jurisdiction at the time of Harry's death."
The judges also rejected Mrs Charles' and Mr Dunn's claim that the Foreign Office "usurped" the police investigation into their son's death, finding that officials "sought to assist rather than obstruct Northamptonshire Police in their investigation".
Asked about the judgement, Mrs Charles said: "Just that it's another blip. It's just another hurdle that they put in the way. We knew that this was a possibility but we always have a plan B.”
The Foreign Office said: “The parties have reached an agreement under which Harry’s family will be protected from paying high costs to the government in respect of the High Court proceedings.”
Radd Seiger, the spokesman for Harry Dunn's family, said they are appealing to the Court of Appeal on "strong legal advice" and are "confident that the ruling will ultimately be overturned in the senior courts".