Materazzi had a rare start against Milan and decided the 1-0 defeat with his mistimed tackle on Zlatan Ibrahimovic.
"You cannot just get over a derby defeat in one day. We took a while, but now it's time to get back on our feet," wrote Matrix on his official website.
"I am the first to say that nobody was burned by this loss as much as me. Losing a derby is doubly painful and those who know me realise it hurts me 10 times as much.
"I am not afraid to admit I made a mistake in that penalty incident on Ibrahimovic, as I was naive and in the end it was decisive for the result. It happens in football, but it wasn't my first mistake and probably won't be my last.
"Each time I have taken responsibility and I do so again now. Once again I turn the page, because anything else would be pointless. One match cannot change a career, despite what some may think."
Materazzi revealed how he deals with the criticism following that derby defeat.
"I prefer not to listen to the critics and have learned that's the best thing. If I were to let myself get knocked down by criticism, I would've retired after the World Cup in Korea and Japan.
"I only have to answer to Inter, my Coach and my teammates. And, of course, to my conscience. I have already done that, so it's time to move on."