The band yesterday (Wednesday) sent "a big bunch of flowers" to the growing tribute near the jazz/soul singer's house in Camden Square, north London.
Meighan said he was broken the news of her death by fellow bandmate Sergio Pizzorno by telephone on Saturday.
He said, "I was really shocked. My body went cold. Before Back To Black came out we had a sing song around hers,... it was great, lovely memories, I was singing one of my songs and then she just sang and I was like 'wow what a lovely voice!' - just nice.
"I saw her at the Q Awards about a year ago and she gave me a hug and a kiss and said are you alright? I am just so sorry. I had a tear, a little tear. I was in shock. My body went cold. I sent over some flowers today to her shrine from Kasabian - where all those people are putting all flowers - a big bunch of flowers from us. I think that's respectful. She was lovely wasn't she?"