The US Embassy told the British government the suspect in a crash which killed Harry Dunn would be leaving the UK, the foreign secretary has said.
Mr Dunn, 19, died after a collision outside RAF Croughton with a car owned by US citizen Anne Sacoolas.
Dominic Raab told the Commons his department asked for her diplomatic immunity to be waived, but the request was refused by the US.
Mr Dunn’s family said the statement “added insult to injury”.
Their spokesman Radd Seiger said there was an “unacceptable lack of information being provided to the family”.
“There is even more anger and frustration tonight than there was before this statement was made in the House of Commons,” he said.
“The statement Dominic Raab gave tonight, he could have given to the family directly when they met with him two weeks ago.”
Mr Dunn died from his injuries when his motorbike and a car collided outside the RAF station in Northamptonshire on 27 August.
Mr Raab said the US Embassy informed his office of the crash and said Mrs Sacoolas was “covered by immunity”.
The Foreign Office requested to waive her immunity “to enable the police investigation to follow its proper course”, he told MPs.
But Mr Raab said on 13 September his office was told by the US “that they would not waive immunity and that the individual would be leaving the country imminently, unless the UK had strong objections”.
He said his office “duly and immediately objected in clear and strong terms” but when they spoke to US officials on 16 September they were told Mrs Sacoolas had left the UK the day before.
The foreign secretary said they immediately informed Northamptonshire Police but asked officers to delay telling Mr Dunn’s family the suspect had left the country “by a day or two” to give them time to “agree the next course of action”.
However, the police force did not tell Mr Dunn’s family that Mrs Sacoolas had gone back to the US until 26 September, Mr Raab said.
Mrs Sacoolas’ husband is reportedly stationed at the base as an intelligence officer.
At the time of the crash she had diplomatic immunity, but both the British and US governments agree that by returning to the US she had forfeited that right.
Mr Raab said he had commissioned a review into immunity arrangements for US personnel and their families at the RAF Croughton annex in light of this case.
“As this case has demonstrated, I do not believe the current arrangements are right and the review will look at how we can make sure that the arrangements at Croughton cannot be used in this way again,” he said.
He said the case was “now with Northamptonshire Police and Crown Prosecution Service and it is for them to consider the next steps as part of their criminal investigation”.
Mr Dunn’s family were due to meet with the Chief Constable of Northamptonshire Police on Wednesday but were told he could not say anything more than offering his condolences.
“They feel completely abandoned by both [the police and the foreign office],” Mr Seiger said.
“This is incredibly stressful and exhausting and gruelling. The family just want answers.”