Pelle was taken off on the hour after an ineffective display in the World Cup qualifier which ended in a 1-1 draw.
"Unfortunately, it's happened again, I've messed things up," the 31-year-old said on Instagram.
"It was unacceptable behaviour, firstly against the coach and also, towards my team mates, who have always shown me to have important values in this fantastic Italy group we belong to.
"Like any great mistake, I accept the consequences. And it is only right that I take responsibility. I must ask offer my apologies from my heart to everyone."
Ventura played down the incident even before the former Southampton player, who is now based with Chinese club Shandong Luneng, had apologised.
"Pelle was angry, I think this was not so much because of the substitution as the way we had played up to that point," he said.
Veteran goalkeeper Gianluigi Buffon was also prepared to forgive and forget.
"He's a great guy and in the cold light of day, I'm sure he will realise he was wrong," he said. "If he apologises for his behaviour, we will be happy to embrace him.
"It was wrong but these things happen in such tense matches."
(Writing by Brian Homewood; Editing by John O'Brien)
