Earlier in the day, Rahman had posted a picture of him sitting at the Nightingale's feet and tweeted: "Love, respect and prayers."
In the video, Rahman talked about the music icon at length. Observering that "it was a very, very sad day for all of us," he said: "Somebody like Lataji is not just a singer, not just an icon. (She is) I think a part of the soul, a part of the consciousness of India, Hindustani music, Hindi poetry, Urdu poetry, Bengali and so many other languages she sang in. And this void is going to remain forever for all of us."
Remembering the respect his father had for Lata Mangeshkar, Rahman said: "My experience with her goes back to my dad (he passed away when I was young), who, I believe, had a picture of her near his bed. So he would wake up and get inspired and go to the recordings. It starts there."
He then talked about his association with the Nightingale, saying: "Coming to me, I was so lucky as to record a few songs with her, sing along with her, be a part of her show, where I learnt probably one of the most important things about performing on stage."
The music director said he had once observed before a live show, after the rehearsals got over at 4 p.m., going back to her room with her assistant and starting to sing each song again.
"Very slowly, every lyric clearly. I just passed that side and asked myself, 'Is that her practising for the show?' That one incident changed my life. After that, every show that I go to, I go out and take up the tambura and practise. Get the warm-ups done. Every lyric coming out, the way it should come out," Rahman noted.
The music director also spoke about the time and effort that the legend invested in each song.
"One day, I was speaking to her and she said, 'Those days, Naushad saab would make us come for 11 days for rehearsal.' I said, 'How long would you take? I'll learn the song immediately.' Still, he would insist that we came for the rehearsal on all 11 days'," Rahman remembered.
And then he commented: "You then understand the depth of each song. It has so much investment of time, love, spirituality, passion. For the younger generation, I think it is so important to lean into something so deeply, believe in it. Give it all. Not expecting any returns.
"This is probably the kind of thing that I learnt from one of the last pillars of last century's legacy of Indian music."
Rahman concluded by saying: "A huge void is going to happen. Even though we have the wealth of her songs, not having her physically is a void which is going to be very difficult to fill in. I know that there are hundreds and thousands of singers who got inspired by her songs and are singing and probably taking it much further in their own way.
"Still, I think the impact, the foundation which her generation has laid -- she, along with Rafi saab, Kishore Da, Manna Dey, Shakeel saab, Naushad saab, S.D. Burman, Salil Chaudhary (all legends) -- is something I really will value for the rest of my life. All we can do is celebrate and learn from this legend who has left us. God bless her soul."