The Nerazzurri struck twice in the opening stages of the game through Nicolo Barella and Romelu Lukaku and that was enough to inflict a humbling defeat on Peter Bosz’s men despite Kai Havertz’s consolation goal.
Conte’s men had two penalties awarded which were overturned by the Video Assistant Referee, and could have scored more if not for their profligacy.
The Serie A side will face either Shakhtar Donetsk or FC Basel in the semi-final on August 17; their first major semi-final since winning the treble in the 2009/2010 season.
Speaking after the game, Conte expressed his delight with his team’s performance and insists they want to go all the way.
“We are very satisfied, because it was a very good performance. We prepared it the right way, never let Leverkusen play the ball comfortably, we did what we worked on in training,” the former Juventus and Chelsea boss told Sky Sport Italia.
“As I always end up saying, we could’ve killed the game off earlier and relaxed a little. We didn’t allow many chances at all, but the fact is we had so many chances and should’ve scored more than two.
“The lads showed how hungry they were, how determined to prove that what they’re doing is important. We’ve got an opportunity to play a Europa League semi-final, so can be pleased, but from tomorrow must begin preparing for the semi-final.
“We want to achieve the maximum. We want to go all the way."