Barella won a penalty for an apparent dive on the day.
After his player apologised, Inzaghi said: Barella deserves credit, it was a lovely gesture.
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"Adrenaline makes you do some bad things sometimes, we coaches are the first to suffer from that, but it's important to recognise mistakes and make up for them."
Barella said after victory over Bologna: "I just want to say that people accused me of simulating against Genoa. It was not my intention to simulate, but if my reaction was a bit over the top or it caused someone to misread the situation, I want to apologise.
"Sometimes, if you really want to win, you do things that you didn't want to or wouldn't want to do. I apologise."