Early goals from Stephan El Shaarawy and Bryan Cristante appeared to have put Roma on course for victory at the Stadio Olimpico, only for the hosts to switch off and offer Chievo a route back into the game.
Valter Birsa pulled a goal back seven minutes after the break, with Polish striker Mariusz Stepinski claiming an equaliser in the 83rd minute.
The draw leaves the 'Giallorossi' trailing in the title race, albeit still early in the season and speaking after the game, Di Francesco expressed his frutration with the performance, particularly with a trip to the Bernabeu on the horizon in midweek.
"I’m disappointed,” he admitted after the final whistle. “The game seemed to be under control but you have to kill off these games. We had the chance to do so but we lacked that killer instinct. The thing that comes out of today is that we concede goals too easily, even when we don’t give away many chances.
“The team played much better with the two central midfielders in the second half and we were able to block their lines of passing. When a match looks like it’s under control, the biggest mistake you can make is to fail to put it to bed. We didn’t manage the game well and it was the same in Milan.
"We must hold onto our mentality. We need to improve when defending because the team is creating a lot and there’s quality to our build-up play. But if you play like that, you have to score four or five goals to ensure you don’t end up under pressure. We didn’t do that today and handed Chievo a lifeline. We can’t do any of that in Madrid. We need to defend well as a team first and foremost, then we can work on producing some excellent attacking play."