Conceicao has been named AC Milan coach this week after the dismissal of Paulo Fonseca.
In Riyadh for the Supercoppa Italiania, Inzaghi said: "Unfortunately, we coaches are always subject to judgment.
"It's a shame for Fonseca because he's an excellent coach and a great person. He hasn't had great consistency in the league, but he played a great Champions League and Coppa Italia match.
"Conceicao played with me and it will be a pleasure to meet him and challenge him as has already happened in the past."