Sean Cole, 26, was swimming with a friend in the Mary River about 100 miles from the Northern Territory capital of Darwin on Saturday night when he was attacked by the crocodile.
More than a dozen friends attending the same 30th-birthday party said they watched as the 16-foot chomper carried Cole upriver in his jaws.
Parks and wildlife ranger Tom Nichols said four crocodiles have been shot, including the one believed to have killed Cole.
"Any animals that were in that range which we believed to be a possible target in the area where the accident took place, we usually take them out for simple reasons," Nichols said. "We do autopsies on those, and it's also closure for the families if there's anything there."
The area where Cole and his friends were celebrating has the highest density of saltwater crocodiles in the world, though Cole's is the first known fatality on the Mary River.
"They sort of know they shouldn't swim there, but they let their guard down," said Grahame Webb, a crocodile expert who said there were adequate warnings of the dangers. Webb said there should not have been swimming at all in the Mary River.
"Parks and Wildlife put a huge effort now into public education, so because we've got a transient population up here it's really important people learn quickly. I doubt there's much more you can do," Webb said.