Former Det Con Evan John Hughes, from Pwllheli in Gwynedd, was one of the first officers to sit with Brady after he was arrested in October 1965.
He recalled taking Edward Evans' mother to the mortuary to indentify her son.
Brady, 79, died at Ashworth Hospital on Monday where he had been detained since 1985.
Along with his lover Myra Hindley, he tortured and murdered five children in the 1960s in crimes that shocked the nation.
He was jailed at Chester Assizes 51 years ago for the murders of Mr Evans, 17, John Kilbride, 12, and 10-year-old Lesley Ann Downey.
In 1985, he also admitted to the murders of Pauline Reade, 16, and Keith Bennett, who was 12.
Following his arrest, Mr Hughes, who was part of the Moors Murders investigation, was asked to sit with Brady in a room until he could be interviewed by senior officers.
"Honestly, you would think that he hadn't committed anything, he hadn't done anything wrong. He was quite cool, reading a newspaper and having a smoke," Mr Hughes told BBC Radio Wales' Good Morning Wales programme.
"He was a hard man and devilish obviously in what he had committed but on the other hand he didn't show this. He was a stern, angry-looking man who said nothing."
Mr Hughes was asked to go and see Mr Evans' mother with a fellow police officer.
"I brought her back to Hyde [Greater Manchester] where she had to go into the mortuary and indentify her son," he explained.
"It wasn't an easy task, it was very difficult. Being the senior of two of us, I had to knock on the door and it was answered by a neighbour.
"I had already lit a cigarette outside the door which showed how nervous I was despite the fact I was a policeman at the time."
He recalled his wife being concerned for the safety of their eldest daughter, who was just 12 months old at the time, as children disappeared "without trace" in the area.
"Everybody was worried stiff, children were afraid to go out," he said.
Mr Hughes described himself as a "small cog in the big wheel" that brought Brady to justice.
"It was an awful experience to go through what we did at that time, for everybody," he added.
"I remember standing on the side of the grave of Lesley Ann Downey and by my side there was a chief inspector from Lancashire county and although it was dark at night, I could see the tears in his eyes.
"He turned to me and said 'hanging has just been stopped and this would have been the only answer in this case'."

Italian diplomat Filippo Grandi, who took over the post from Portugal's Antonio Guterres this year, was speaking on a visit to Lebanon.
Mr Grandi also urged the EU to do more for Syrian refugees outside Europe.
EU leaders have warned of a crisis after more than a million migrants entered illegally last year.
French Prime Minister Manuel Valls told the BBC this week: "If Europe can't protect its own borders, it's the very idea of Europe that could be thrown into doubt."
On Friday, his Dutch counterpart, Mark Rutte, warned: "When spring comes and the numbers quadruple, we cannot as the EU cope with the numbers any longer."
The new UN High Commissioner for Refugees has been meeting refugees in camps in Lebanon and Jordan.
Speaking to the BBC's Quentin Somerville, Mr Grandi said: "Europe can absorb more genuine refugees if it would be better organised among the different member-states.
"However, we understand the predicament. It is a social and political predicament which is very serious."
The EU is drawing up plans to share the "burden" of refugees more evenly among member states, scrapping a controversial rule that means they must claim asylum in the first country they arrive in.
Hungary, one of the most vocal critics of migration policy, has dismissed the crisis as a "German problem" since Germany is where those arriving in the EU "would like to go".
Mr Grandi also urged the EU to "do more for the countries of first asylum" so there would be "less motivation for people to flee further away".
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A detective constable sent to speak to the family of a Moors Murders victim has described Ian Brady as "devilish".
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EU states could take more genuine refugees from Syria if they worked together better, the new head of the UN refugee agency has told the BBC.