Arturo Vidal and Nicolo Barella scored the goals as Inter deservedly triumphed at San Siro last month, the defeat inflicting further damage on the reigning champions in their bid for a 10th straight Serie A title.
However, since that setback in Milan, Juve have won four games in a row without conceding. That run includes lifting the Supercoppa Italiana at the expense of Napoli, as well as a Coppa Italia quarter-final success over second-tier SPAL.
Next up in the competition is a two-legged tie with Inter and, having been second best in the previous meeting, Pirlo is confident his side learned a valuable lesson from that game.
"I want to see a team aware of their strength," Pirlo - who confirmed Gianluigi Buffon will start in goal - told said.
"It will be the first round, because it's a 180-minute game, so tomorrow it will be important to manage it well, because it won't be decisive.
"The match against Inter in the league taught a lot, first of all, when we are not on the right track, we are not ourselves, but from there we started with great performances.”
As for Conte, he is wary of a repeat of what happened to Inter in the competition in the 2019-20 season, when they lost 1-0 at home to Napoli in the first leg of the semi-final. A 1-1 draw was not enough in the return fixture, meaning they were knocked out by the eventual winners.
"You always need to be very respectful of very strong teams, and we'll certainly need to put in an excellent performance,” the former Chelsea boss told the media.
"The upcoming 180 minutes will determine who progresses, and the first match will be important. Last year, we lost 1-0 to Napoli at home and didn't manage to turn things around at the San Paolo despite playing very well. We will need to perform and try to do our best."
The Nerazzurri will be without Romelu Lukaku on Tuesday due to suspension after he received a yellow card for his part in a confrontation with Zlatan Ibrahimovic in the previous round.
Conte, though, is confident he has enough strength in depth at the position to cover for the absence of the influential Belgian. Lukaku scored twice at the weekend against Benevento in Serie A action, taking his tally for the campaign in the league to 14 goals in 16 appearances.
"It's not the first time that Romelu has been missing," Conte said. "We will have Alexis and Lautaro, who I'm sure will do well.
"Romelu is feeling good, he responded on the pitch and scored two goals against Benevento. Now, he's being forced to rest due to his suspension and will work hard to be in good shape when he returns in the league."