"I am sorry above all to have lost a great personality in the coach (Ancelotti) for what he has given to everybody," said the Italy international.
"He has already won everything there was to win and has a wealth of experience."
However, Zambrotta claims there is one way in which Ancelotti can improve.
Ancelotti is embarking on his first adventure outside of Italy and, if his first official interview as Chelsea coach on Monday is anything to go by, he still has a lot of ground to make up in his grasp of the English language.
"Above all, he needs to improve his language skills because I heard him talking and his English is still a bit at schoolboy level," Zambrotta told Sky television with a wry smile.
"Joking aside, he is a great coach and I don't think there is much advice you can give him."