The Giallorossi emerged victorious thanks to Marco Tumminello's last-gasp strike, having managed to squander a two-goal lead just minutes earlier.
As with the opening International Champions Cup match against Paris Saint-Germain the coach was not unduly concerned about the result, preferring to focus instead on the tactical elements on show.
"In the first 30 minutes my team really pleased me a lot," Di Francesco said. "It is normal that, at this point, it's not possible to maintain the levels for the whole game.
"We have done well in possession and pressing against a strong, settled side that has a great record in the Premier League ... I'm not so happy about a few things towards the end of the game, but in general I'm pleased with the progress shown."
The game was perhaps especially notable for the impressive debuts from Gregoire Defrel and Aleksandar Kolarov, while Cengiz Under came off the bench in the second half and grabbed a valuable goal.
"Defrel is improving physically, and tonight he played in a role that isn't his favourite," Di Francesco said. "In a few situations he wasn't quite able to do what he wanted.
"Cengiz has shown he has a lethal touch... we want to have two players for each role. Kolarov was great in his technical ability and for his personality."
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