Goals from Cristiano Biraghi and Romelu Lukaku earned Inter a 2-1 victory at an empty San Siro after Cauly opened the scoring for Ludogorets, who trailed 2-0 from the first leg.
Fears over the coronavirus outbreak in Italy meant supporters were not allowed to attend the match and Inter head coach Conte admitted the tie had an eerie feel to it.
"I've also played behind closed doors with Italy against Croatia," he told Sky Sport Italia.
"The atmosphere is strange and doesn't make things easy as it's like a training session. I have to say that my players took the right approach today, even if we fell behind. We made changes, giving other players some minutes, and now we move on."
Serie A have also confirmed that this weekend's
Conte's Nerazzurri lost their last league match 2-1 to second-placed Lazio and trail Juve by six points with a game in hand to play, with the Italian