The Giallorossi took control of their Champions League destiny with an emphatic home win - as Stephan El Shaarawy (twice) and Diego Perotti grabbed the goals.
And Di Francesco was delighted with what he saw - hoping it is a sign of what is to come from the squad.
“We knew we might struggle today with the formation Chelsea went with but we also knew we could hurt them on the counter and so it proved," Di Francesco said. "The lads dug in and defended really well when they needed to, which is exactly what all great teams must be able to do.
"We've shown that we're an improving side. We mustn't stop now, though. We have to push on from here.
"We need to take this spirit with us in all competitions across the campaign - and if we do I am convinced we can achieve something important."
Do you feel you've proven a point tonight on a personal level?
“I don't feel I need to prove anything but I do believe in hard work and I believe in my ideas. The lads took a while to get to grips with what I want from them but they've always been very willing and now we're reaping the rewards. We're making progress and it's not just the guys who played tonight but everyone who's training the right way. Whoever goes out there knows what they have to do.”
Was Alessandro Florenzi just tired?
“He was knackered. I asked him if [being substituted off] was his way of getting some applause from the crowd! It's quite understandable though: he's come back from a long injury lay-off and when you play so many games one after another you start to feel it. When he was out there, he looked like the Florenzi of old.”
What have you done to Stephan El Shaarawy?
“He's done it himself. He's training well, playing consistently and he's always involved in the game – he never looks isolated on the wing. I like it when he comes inside and you could see why today. He made two runs and scored two goals. That's what I want from my wide players. He did it from the right today whereas he usually plays on the left. I'm delighted with our improvement.”
Were El Shaarawy's runs the key to hurting Chelsea?
“Yes, I think they were. There was a slight mistake on the second goal but he kept believing and chased the ball. I like wingers who cut inside to receive the ball – I think there are lots of benefits to be had, as we saw today.”
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