Exercise Diamond Dragon was a joint UK/US emergency exercise staged at RAF Honington in Suffolk last summer.
The scenario involved a C-17 releasing radioactive material after crashing.
The Ministry of Defence report found a number of issues including IT and communications, but the US deemed it a success.
The three-day operation included various public bodies, the government and the military from both the UK and US.
The report said there were difficulties in understanding because the exercise "involved a wide range of agencies, including US personnel, all bringing with them their own terminology and acronyms".
"To ensure a clear understanding by all participating agencies, the use of plain English.......should be used," it said
The report said at the very least, terms listed in the Civil Contingencies Lexicon, should be used by those taking part in such exercises in the future.
Examples include:
Source: Civil Contingencies Lexicon
It also found the combined fire control "had difficulties in understanding the initial information passed to them" and "poor information flow between agencies" because of the various IT systems different organisations used.
Suffolk County Council, responsible for the county's fire service, declined to comment on the findings.
One of the UK's computer systems failed temporarily "due to extremely hot weather", the report found, which meant "only one laptop" was available to write a weapon recovery plan on, which "did not have the needed templates".
A spokeswoman for the United States Air Force in Europe said: "Overall, Exercise Diamond Dragon was a success.
"We fully expected to discover a few challenges along the way.  That's precisely why we conduct these types of training and exercises.
"In particular for bilateral exercises, you want to discover where the shortfalls occur while also identifying where we already integrate seamlessly."
Lessons learned from the exercise included teaming and training with civil emergency responders, performing rescue operations and providing advice to incident commanders on hazard priorities, she added.
A mock exercise in which a US aircraft carrying a nuclear weapon crashed over England has revealed the importance of "plain English", a report has found.