Gattuso has replaced Luciano Spalletti with the Azzurri's chances of reaching the tournament next year in the balance.
The AC Milan icon told Sky Italia: "There is great satisfaction and pride. We have a lot of hard work ahead of us and we hope it goes well. There is no room for mistakes: the standings speak clearly.
"There is no margin for error, I have it well in my head, I will have to convey it to the players.
"Everyone thinks that players today are spoiled but they are clearly more professional than when I played. I have a very high regard for them now I have to be good at transmitting the concepts of group to them because in moments of difficulty the teammates can always help."
On the amount of foreigners who play in Serie A, Gattuso continued: "In recent years at youth level we are achieving incredible results and then they are lost.
"The 68% of foreigners is a high figure and our Italian football suffers from this. I have to choose the players that the championship makes available to me."
On how Italy reach the World Cup, he added: "By winning matches and being convincing with your performances: there is no other way."