It is not the first time Mr Farrell has been abducted on assignment - in 2004 he was briefly kidnapped in Iraq while working for the London Times newspaper.
In remarks quoted on the New York Times website, Mr Farrell said the Taliban tried to flee as the helicopters descended.
"There were bullets all around us. I could hear British and Afghan voices," he said.
The reporter told his newspaper he ran outside with Mr Munadi, reportedly a 34-year-old father-of-two who worked as an interpreter with Mr Farrell.
He said Mr Munadi had shouted "Journalist! Journalist!" before he fell to the ground in a hail of bullets.
Mr Farrell said he did not know whether the shots had been fired by their rescuers or the militants.
Afghan police inspect the car from which Stephen Farrell and Sultan Munadi were kidnapped
"I dived in a ditch," Mr Farrell told his newspaper. Moments later he heard British voices and shouted: "British hostage!"
The voices told him to come over and as he did, he said he saw Mr Munadi's body.
The head of the Afghan Independent Journalists' Association, Rahimullah Samandar, told the BBC that the raid showed international forces did not care about Afghan reporters.
Mr Samandar said it was not the first time a kidnapped Afghan journalist had been killed while a Western colleague was freed.
Bill Keller, executive editor of the New York Times, said the newspaper was "overjoyed" at Mr Farrell's release, but "deeply saddened it came at such a cost".
Chris Morris, BBC News, Afghanistan
There is concern among the Afghan media community that Stephen Farrell was rescued unharmed but Sultan Munadi was killed.
Now the Afghan information minister has called for an inquiry into the circumstances of Mr Munadi's death.
Two years ago, an Italian journalist was released from captivity, but his Afghan colleague, Ajmal Naqshbandi, was beheaded by the Taliban after the Afghan government refused to release Taliban prisoners in exchange.
The international media rely heavily on Afghan journalists to cover areas of the country which are too dangerous for foreigners to visit. But in this most recent case, of course, Stephen Farrell had travelled with his colleague to Kunduz where they were kidnapped.
Reports differ on who else died in the raid, but a local governor told the BBC two civilians were killed.
A resident of Char Dara district in Kunduz province, Mohammad Nabi, reportedly said it was his home that was raided, and that his brother's wife was killed.
The Taliban had turned up there on Tuesday night with their two captives, demanding shelter, Mr Nabi told Reuters.
He said helicopters swooped later and "then the soldiers blew open the door of my house, killing my sister-in-law, and took the reporter away with them".
UK Prime Minister Gordon Brown said the soldier killed in the British-led operation had acted with "the greatest of courage".
He said his thoughts were with the family of the soldier and also with Mr Munadi's loved ones.
Mr Munadi had briefly returned to Afghanistan while studying for a masters degree in Germany.
In an article published by the New York Times, he wrote of his desire to return to Afghanistan.
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.