Juve suffered a 2-1 defeat in the reverse fixture at the Santiago Bernabeu after Giorgio Chiellini was given a harsh red card.
A victory at home would give the Italian side's hopes of qualifying a huge boost, and Conte believes that the fans could make the difference on the night.
"I hope the Juventus Stadium is going to be a boiling cauldron on Tuesday night, so that the fans can push us to victory," the 44-year-old coach told Juventus TV.
"We have already shown in Madrid what we can do. Madrid have been constructed to win their 10th European Cup, but we must not be afraid."
The Serie A champions sit third in Group B with two points from three games.