The incident took place on Saturday at the Stadio Olimpico after the Rossoneri's 0-0 draw at Roma ensured the title.
"I always take responsibility for myself," the 2006 World Cup winner told La Repubblica.
"All this fuss for a prank seems exaggerated. If I could go back in time, given all the mess it has caused, I wouldn't do it again."
Leonardo himself went as far as issuing a statement on the Inter website yesterday, while Nerazzurri chief Massimo Moratti also criticised the player.
"I exaggerated and I realise it was not a good example to set for the kids," Gattuso continued. "But it's not right to forget the context.
"The fans in the Curva sang many other songs, at least nine, and you don't hear educational chants at the stadium. But let me be clear, I would jump on the railings to sing with them again.
"Those fans have followed us around Italy, facing so many expenses and journeys. The least we could do was thank them.
"There are all sorts of people among the Ultras. To demonize them would be hypocrisy."