The Serie A side won the round-of-16 first leg 2-1 at the Stadio Olimpico but were beaten 3-1 in the return after extra-time, which secured a 4-3 aggregate victory for Sergio Conceicao's side.
Di Francesco took over from Luciano Spalletti in the summer of 2017 after a spectacular run with Sassuolo. He took the minnows up to Serie A and even into the UEFA Europa League, cultivating several talented players along the way.
He never fully seemed to settle in the capital, however. A magical run to the UEFA Champions League semi-finals in 2018 largely overshadowed a disappointing domestic campaign, as the Giallorossi finished a distant third behind Juventus and Napoli.
Plenty of turnover followed in the summer―Radja Nainggolan, Alisson Becker and Kevin Strootman were among the departures―and after a narrow 1-0 win over Torino to start the season, Roma endured a nightmare spell.
A 3-0 loss against Real Madrid in the Champions League didn't come as a surprise, but in Serie A, the Giallorossi performed well under expectations.
Perhaps the worst result came against Bologna, who entered the match having failed to score a single goal only to beat Roma 2-0:
Roma's form did pick up, and the club are fifth in the Serie A table and three points behind Inter Milan in fourth.
However, Saturday's damaging 3-0 defeat to Lazio, coupled with their exit from Europe's top club competition, led to the end of the road for Di Francesco at Roma.