Shop
The Giallorossi are in Group C of the competition alongside the reigning Premier League champions Chelsea and Atletico, who reached the final in both 2014 and 2016.
Qarabag complete the group - and Di Francesco knows Roma are in for a stern test.
"I watched the draw along with the squad, and I have to say you are always hoping for something good - and you know you always have the chance of playing important teams like Chelsea and Atletico," Di Francesco said. "Qarabag may be considered weaker, but these are games that cannot be taken for granted.
"It's a difficult group, but we were in the third pot and we knew that some big teams were waiting for us."
The boss is looking forward to testing his tactical wits against Chelsea boss Antonio Conte and Atletico's Diego Simeone.
"Chelsea have a great coach who I know really well, a squad full of top players and with [Alvaro] Morata they have added quality," he noted.
"With Atletico, when you think that in the last four years they have made two finals, it means they know how to play in these competitions. The coach has great strength ... beyond the quality of the squad, being able to work with the same coach for so many years gives you real stability.
"We have respect for every team in the group but we will do as well as we can in every game."
Imperium Partners
Centurion Partners
