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The Giallorossi emerged as victors in the International Champions Cup game in Dallas - thanks in large part to a second half surge.
While content with the performance, Di Francesco was not placing too much emphasis on the result.
“Tonight we played against a side with great talent on the ball, which had us in difficulty at times," Di Francesco said.
"But when we found the right urgency and won the ball high up the field a few times, we started to do well. This sort of thing is vital when you play a side like Barcelona."
He added: "We are at the end of July now and our fitness levels aren’t at 100% yet. Barcelona certainly have some more spritely players, and we saw that. Tonight we saw their ability with the ball, but at the end of both halves we finished well. But that's normal; if we were in top shape now I’d be more worried."
After losing to Tottenham Hotspur 4-1 last week, Di Francesco was relaxed about the apparent inconsistency of performances at the moment.
“Right now the line between something done well and something done badly is very fine," he said. "I’m happy with what the guys are doing, but preparation is vital right now: building on the quality the guys have shown during training.
"The team that does the best is the one that makes the fewest mistakes. And we know in that regard we have to keep improving."
The boss also answered questions on the transfer market - downplaying a suggestion that he still wants a number of quality additions to the squad.
"I don't want a squad that is too big; Monchi is not sleeping and is working from morning until night on the market," Di Francesco said.
"We are looking at things and making assessments, but I think we have a great side here already. Decisions will be made without panic. I don’t want to have 30 players, it would make it hard to treat the lads fairly - all of them deserve to play.”
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