The crew's trade union, the Allied Pilots Association of America, decided to release the interview as part of a training exercise for other pilots - despite objections from American Airlines.
Richard Reid is due back in court on Thursday for a pre-trial hearing in Boston, where it will be decided what evidence can be admitted to his full trial which is due to start later this year.
He has pleaded not guilty to charges of attempted murder and attempted use of a weapon of mass destruction for trying to blow up American Airlines Flight 63 from Paris to Miami.
Mr Reid was overpowered by passengers and sedated by an onboard doctor until the flight was diverted to Boston's Logan Airport, where he was arrested.
The American Airlines flight was halfway across the Atlantic when Richard Reid allegedly tried to set fire to explosives concealed in his shoes.
One of the pilots identified only as Kent describes how he removed Mr Reid's shoes and foolishly took them into the cockpit.
"I got the shoes, showed them to him, said: 'Are these your shoes?'; he said 'Yes', and I took him up to the front, and one of the dumbest things I ever did was call the cockpit to say I'm coming in with something," he said.
"On the way in there, they had to open the door to find somewhere to sit down, I realised and maybe they realised at the same time I do that I smell the cord, think 'Oh my gosh', this is what he was trying to light, this is now not a shoe and a weapon, this is a bomb."
Mental state
The court on Tuesday heard conflicting accounts of Mr Reid's mental state.
At the pre-trial hearing, his lawyers said interviews conducted by the FBI after the plane made an emergency landing should not be admitted as evidence because Mr Reid was affected by sedatives administered by fellow passengers after he was overpowered.
But an FBI agent who questioned Mr Reid said he spoke clearly and confidently.
That view is disputed by a defence witness - a paramedic who said Mr Reid appeared intoxicated.
Richard Reid, who is originally from London, faces eight charges. His trial is expected to begin in early November.