Los Blancos ended a 12-year wait for their 10th European crown in May by overcoming rivals Atletico Madrid 4-1 in extra time.
And the Italian says that that sort of togetherness is vital to Italy's chances in Brazil as they attempt to navigate a group including England, Uruguay and Costa Rica.
"People are sceptical about Italy's chances and do not believe in us," Ancelotti wrote in La Gazzetta dello Sport.
"I can guarantee that, if the team and the coaching staff stay united and all read from the same page, then the atmosphere will become more favourable and results are more likely to go our way.
"That is how Real Madrid won the Champions League. That's why now it's important to encourage Italians to get behind our lads."
The former Chelsea, Juventus, AC Milan and Paris Saint-Germain coach added that the Azzurri face a tough group but insisted that the experience in the squad can see Cesare Prandelli's men through to the knockout stages.
"One thing is for certain: facing Italy is difficult for every team," he remarked.
"We are a strong team tactically, we are experienced and we have players that can make the difference."