The Verve frontman, 47, came under fire after debris fell from his pocket while guest appearing on the Saturday morning football show.
Viewers shared the moment online with many claiming he picked up a packet of drugs.
Ashcroft was quick to shut down all speculation, telling “trolls” to not “libel my name”.
Speaking on Instagram he said: “Just a quick message to a couple of you trolls on Twitter who are making a name for yourselves out of me – and also people moralising and virtue signalling.
“Number one: Cocaine and I have had no relationship for decades. Number two: Don’t you ever surmise what has fallen out of my pocket. And, don’t bring my children into it.”
Richard Ashcroft on Instagram pic.twitter.com/sDUvnhgXdp— Mainly Oasis (@MainlyOasis) September 22, 2018
He continued: “You’re on thin ice. Don’t libel my name. My dad didn’t like litter and I don’t really like litter. But it gets a bit preposterous in my pocket. In The Verve I was known as Colombo, so get your facts right. You’re on thin ice. Peace.”
Ashcroft later joked that he should have filmed himself picking up litter for his latest music video as footage from Soccer AM amassed over half a million views.
“Ha 635k thousand people watched some paper fall out of my trousers ha,” he tweeted. “Should have done this for my video.”
Ashcroft was on the show to discuss Anthony Joshua’s first world heavyweight title fight against Alexander Povetkin.