The flanker was an ever-present for the Azzurri, who will travel to South Africa this summer to take part in a tournament also featuring the Springboks, Samoa and Scotland.
And Zanni is desperate for the team to carry the momentum of the RBS 6 Nations into that summer tour.
He said: "It was a brilliant tournament for us, especially the games against France, England and Ireland.
"To win two games and match our best performance was great and for me to get the recognition with the voting in the player of the tournament was very special.
"But we have a big tour to South Africa with the games against them, Samoa and Scotland and we want to perform like we did in the Six Nations.
"It will be very difficult but a great opportunity for us."