Acerbi joined the Nerazzurri on loan in the off-season, with an option to buy, and was relieved to part ways with Lazio after his relationship with the club and supporters deteriorated.
The 34-year-old insisted that his exit was not due to head coach Maurizio Sarri, whom he admires, but rather an incident which was blown out of proportion.
After scoring in the 3-1 win over Genoa in December last year, Acerbi put his index finger to his mouth as a 'keep quiet' gesture.
This was directed at the Lazio fans who had been booing the team in previous games.
Acerbi later apologised for the gesture, but it seemed that the relationship was already over as Lazio did not come to the player's defence.
"Let's start at the end. I would have stayed for life, otherwise I wouldn't have signed for five years. But it was still me who wanted to leave. And in June I told Sarri, who wanted to keep me. I had been delighted with his arrival," Acerbi told Corriere dello Sport.
"And I have nothing to say about his value as a coach, on the contrary, he's great, he's strong and he thinks about football 24 hours a day. But I didn't feel suited to what he wants from a central defender.
"I wanted to have fun, to do what I like on the pitch, I need to anticipate the opponent, to read the game. Sarri, on the other hand, has his system and either you do this or you do that. Mind you, though, I've always given everything, never sparing myself.
"As I gave my all, so did my teammates. We struggled, though. And they booed us. After the goal against Genoa I put my index finger in front of my mouth, making the gesture to keep quiet. It wasn't appropriate, so I apologised.
"It wasn't enough, at that moment something broke. I have a fiery character and I care about what I do. It would be easier to be an a*****e, but I'm not like that. In the last year I have had to eat a lot of s**t.
"I made one mistake, but that's worth five compared to the 95 I had to swallow. I still went on my way, putting my face to it and not giving a damn. And I am very proud of that.
"Others, in my place, would have quit much earlier. I expected the club to defend me, absolutely. You can make mistakes, but the club has to protect you in public. Even if they slaughter you in private."