The 38-year-old was taken off the Tour and suspended by his Katusha team on Friday evening after returning a positive result for cocaine from a test conducted on Tuesday.
Paolini apologised to Tour organisers and his own team but neither admitted to the offence nor denied it in a long post on Twitter.
"Excuse me but I've had to absorb the blow! I believe and always have believed in the controls, they are making this sport more credible, ever more so," he said.
"I wanted to stay silent and resolve this thing in my own way!! I'm not the type to scream of a scandal and hopelessly try to run away.
"And as for what's happened, I take full responsibility and will look to clarify this as best as I can! I apologise to all my colleagues, riders and of course @tour, ASO, knowing that it was the least appropriate moment, especially due to the very high media concentration.
"I apologise to my fantastic teammates at @katushacycling and I hope that my absence won't prejudice a good final result..."
Over the coming days I'll do what I can to understand how it was possible... But there's one thing I want to clarify! There's enough evil in the world to undo. But there are even more people who like me! Hence f*** off those who criticise freely and I hope, with collaboration from the UCI to clarify as much as possible what happened!"
"Good night to the envious and especially to those who've proved to be friends. Once again I'm sorry."
Katusha said they were "surprised because cocaine is not a substance that improves performance", but said they were following UCI regulations and had suspended Paolini.
The use of cocaine outside of competition is not banned but when taken in competition it is considered a doping substance.
Paolini's was the first positive test at the Tour since Frank Schleck in 2012, who was caught taking a diuretic, which can be used as a masking agent for other banned substances.