Roma appeared to be containing the hosts well until Daniele De Rossi netted a spectacular own goal to undo the Serie A side's hard work.
Di Francesco's men still had their chances, though, and could have at least been level before Barca scored twice in quick succession to move 3-0 in front and seemingly out of sight.
Again Roma rallied and Edin Dzeko scored, but Luis Suarez responded and the scoreline makes for difficult reading for Di Francesco and his players.
"I think the result is too harsh given our performance, considering who we were up against," he said. "We made some small mistakes inside our area and were a bit slow dealing with some situations.
"It's a pity, but we didn't do ourselves justice. We needed to be a bit more clinical because you don't get many chances against Barcelona."
Ter Stegen made a string of late saves and, on the Barca man, Di Francesco added: "People always say how good our goalkeeper [Alisson] is, but don't we want to say something about how good their goalkeeper is too?
"Barcelona are a great team and they also have a great goalkeeper."
Alisson encouraged his team-mates to lift themselves and kick on again after the disappointment of a humbling in Catalonia.
"Mistakes are part of football," he said. "We work hard so we don't make them but in games they are going to happen. We have to keep our heads up and continue to work even harder."