Nainggolan was aggrieved over Friday's defeat to the Bianconeri.
"It went well that they played on 'home' turf! Because if we were at our house, it would've been a different situation Oh well!" wrote Nainggolan on his Twitter account.
"The Juventini insult me after a game they won. How laughable!! But they couldn't hear their fans crying to the referee.
"They won the game and still talk like this But how they cried and moaned when trailing."
Juve supporters then confronted Nainggolan on Twitter and the Belgian international midfielder responded.
"You don't even know the ball is round. :) You win and then offend people. You lose and it's even worse "
Another fan suggested Nainggolan criticised Juventus, but would run to Turin if an offer arrived.
"Yeah, that's why I said no in January. :) "