Juve suffered a 2-1 defeat in the reverse fixture after Giorgio Chiellini was harshly sent off and sit third in Group B with just two points from three games.
However, a home victory over Real would significantly boost the Italian side's hopes of qualifying from a group that also features Galatasaray and Copenhagen.
With that in mind, Conte expects strong support from his team's supporters.
"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 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."
Conte confirmed neither Mirko Vucinic or Stephan Lichtsteiner will be fit to face Real.
"They haven’t trained with the rest of the side yet and, to be honest, I don't know if they'll be back for (next Sunday's match against) Napoli either."
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