NATO did not confirm the cause of the crash but it comes as Afghan forces — backed by NATO special forces and US air support — pushed into the centre of the northern city of Kunduz which was captured by the Taliban on Monday.
“Our mujahideen have shot down a four-engine US aircraft in Jalalabad,” Taliban spokesman Zabihullah Mujahid said on Twitter.
“Based on credible information 15 invading forces and a number of puppet troops were killed.”
The Taliban are known to make exaggerated battlefield claims, and NATO has so far not given details on the cause of the crash.
The C-130 crash, which occurred at about midnight local time on Friday (1930 GMT Thursday), left six US soldiers and five civilian contractors dead, US Army Colonel Brian Tribus said.
The contractors had been working for “Resolute Support”, the NATO-led training mission.
Jalalabad is situated on a key route from the Pakistani border region — where many militants are based — to Kabul, and it has been the scene of repeated attacks in recent years.
Its airport is home to a major military base.
Although NATO gave no immediate indications that the plane crash was due to militant action, Jalalabad airport has come under attack on several previous occasions.
The C-130 Hercules is a cargo plane built by Lockheed Martin. It is powered by four turboprop engines and is used extensively by the military to ship troops and heavy gear.
It can take off and land on rough, dirt strips and is widely used by the US military in hostile areas.