The German shocked the football world by calling time on a nearly nine year stay at Anfield.
Klopp has left for a sabbatical from the sport, with Dutchman Arne Slot taking his place.
Ancelotti told Il Giornale: "I don't see any particular news, this has always been our job but the Klopp case is significant.
“The continuous pressure, the load of responsibilities become excessive burdens, the obsession takes over. It also happened to Arrigo Sacchi."
When announcing his exit reasons, Klopp said: “It is that I am, how can I say it, running out of energy. I have no problem now, obviously, I knew it already for longer that I will have to announce it at one point, but I am absolutely fine now. I know that I cannot do the job again and again and again and again.
“After the years we had together and after all the time we spent together and after all the things we went through together, the respect grew for you, the love grew for you and the least I owe you is the truth – and that is the truth.”