De Zerbi, now in charge of Tottenham. left OM by mutual consent after falling out with the top brass.
Medina told RMC Sport: "For me, it deeply annoyed me, I was furious.
"It bothered me a lot, I told Roberto.
"He and I have a very sincere relationship because we have somewhat similar backgrounds. We share a similar childhood and this fire or this passion that lives within us.
"That's why it hurts me so much when I know that some people make sacrifices to support us, and we can't reciprocate that investment."
He continued: "His departure hurt, it was disruptive, but it's our responsibility to continue our mission. We couldn't control it, we have to take responsibility for our mistakes.
"I came here to be part of a project. Six months later the coach left, then the president, and soon (sporting director) Medhi Benatia...
"These are blows that hurt, and we're human beings, we can be affected. But personally, it will never stop me from stepping onto the pitch with the desire, the hunger, the will, and the right attitude."