BBC News has approached Martin-Smith for a comment.
On the issue of his drug-taking, Williams told his former manager: “Allow me to respond to your assertion. My drug taking was never your fault.
“My response to the warped world that surrounded me is solely my own. How I chose to self-medicate is and was something that I will be monitoring and dealing with for the whole of my life.
“It’s part of my make-up and I would have had the same malady had I been a taxi driver.”
In the documentary, Martin-Smith also said Williams had made him out to be “evil” and had blamed him for some of his behaviour.
Responding specifically to that, Williams said he wanted to remind Martin-Smith that he was just 16 when he joined the band, and 21 when he left.
“That was the last time I saw you. I hope I have more grace and understanding when and if any of my own four children at such a vulnerable age behave in the same manner.”
Williams, who has since forged a successful solo career, also used his post to speak more generally about the pressures of being in a boyband.
“Nearly all members of boybands it seems have at some point a mental breakdown,” he said.
“Your young charge at this time in his life was experiencing his first. You didn’t excel in man management and it was here that, instead of a stern word and a pointed finger, an arm around the shoulder and a kind word would have been the best tact.”
He added: “If you are following the story closely, you can’t help but notice a pattern emerge. Boys join a boyband. The band becomes huge. Boys get sick. Some are fortunate through a series of self-examinations and help to overcome their experience. Some never quite manage to untangle the mess of the wreckage of the past.
“I’m not breaking anyone’s anonymity by sharing the side effects of boyband dysphoria that relate to just us lads.”
He went on the outline the struggles his bandmates have had in the past, including Gary Barlow’s battles with an eating disorder and Mark Owen’s struggles with alcohol abuse.
Returning to his former manager, he told him he had “deep admiration” for his work and his ability to take big risks.
But he added: “Nige, you continue to not come across as a relatable character and could do with a glow-up where redeemable features are concerned. Therefore you play into the narrative you don’t want for yourself.”
He went on to urge Martin-Smith to take accountability and to “admit your shortcomings”.
The documentary, which reaches its conclusion this week, focuses on some of the biggest boybands to grace the charts during the 1990s and early 2000s.