Harry Dunn, 19, died after a road collision near RAF Croughton, an air force base in Northamptonshire in central England that is used by the United States.
"I wish to offer my condolences to the family affected by this tragic incident," Foreign Secretary Dominic Raab said in a statement.
Police said they had applied for a waiver from diplomatic immunity to allow investigations and an interview.
"Unfortunately we were latterly advised that the waiver had been declined and the suspect had left the UK," Northamptonshire Police Superintendent Sarah Johnson told Sky News television.
Raab said he regretted the U.S. decision.
"I have called the U.S. Ambassador to express the UK’s disappointment with their decision, and to urge the Embassy to re-consider it," he said.
A spokesman for the U.S. Embassy in London said: "Any questions regarding a waiver of immunity with regard to our diplomats and their family members overseas in a case like this receive intense attention at senior levels."The U.S. Embassy continues to be in close contact with the appropriate British officials."