The most recent attempt to lift the Champions League trophy ended in disappointment under Jose Mourinho as Borussia Dortmund edged Los Blancos out of last season's semi-finals.
Real had perhaps ridden their luck to get that far after coming undone in Istanbul in the previous round, where Galatasaray pulled off a shock 3-2 win only to exit the competition 5-3 on aggregate due to their poor first-leg showing.
Ancelotti's first continental assignment takes him to the Turkish capital in a group which will also be contested by Juventus and FC Copenhagen, and he hopes the inevitable hostile reception does not dampen his players' desire to claim an opening-night victory.
The Italian told a press conference: "It is the most important competition, all of us want to win it and there is harmony among us.
"We have a team with a lot of quality but, despite that, we are playing in a stadium where the heated atmosphere puts a lot of pressure on you and helps the home team out.
"It will be a very good test for the character of our team."
The departure of playmaker Mesut Ozil to Arsenal had the potential to upset Real fans but his sale has been offset by two impressive pieces of business at the Bernabeu.
Wales winger Gareth Bale arrived for 100million euros before Cristiano Ronaldo finally quashed speculation linking him with a return to Manchester United by signing a new long-term contract.
Ancelotti added: "In the world of the Madrid fan, Ronaldo's contract renewal is very good news because Real Madrid will be able to count on the most important player in the world for many years to come.
"But we still need to play well, to win games and to improve the quality of our game.
"Cristiano will be more motivated to do that now and I hope his performances remain as good as they have been over the last few years."
Former Tottenham star Bale scored on his Primera Division debut at Villarreal but only completed 60 minutes due to poor fitness and, while Ancelotti is unlikely to start the 24-year-old against Galatasaray, he expects to use him at some point.
"He can play in all attacking positions," Ancelotti added. "He's not a natural striker but he can play on either the right or the left. The other day he started on the right because that's the position he likes."
Goalkeeper Iker Casillas has been promised a first start of the season - a reward for biding his time while Diego Lopez minds the nets in La Liga.
Ancelotti added: "I have two very good goalkeepers with fantastic attitudes. Diego deserves to play in the league and Iker - because of his professionalism, reliability and competence - in the Champions League."
Midfielder Xabi Alonso will definitely miss out with a broken foot while Galatasaray boss Fatih Terim has concerns over defender Semih Kaya and midfielder Hamit Altintop.
Ivorian striker Didier Drogba, who worked with Ancelotti at Chelsea, said: "The last time we played Real Madrid we beat them.
"I am optimistic.
"We have very strong teams in our group and we want to get out of it by playing good football. Hopefully I can score more goals."