The incident marred a 2-1 Serie A win in which Cristiano Ronaldo scored his first goals for the club.
Ronaldo could easily have had a hat-trick but missed two more good chances and had a penalty appeal turned down.
As Sassuolo pulled back a goal late on, Douglas Costa pulled Di Francesco to the ground in the build up to that ultimately inconsequential goal.
Senegalese striker Khouma Babacar headed in a consolation goal for Sassuolo in injury-time as the side from Modena fell to their first defeat of the season.
"I would like to apologise to all Juventus fans for this misleading reaction in today's game".
Ronaldo scored 44 goals for Real Madrid last season including 15 in the Champions League on the way to a third straight title.
"It was a bad mistake, I am aware of it and I apologise to everyone for this". I make it clear that this isolated attitude does not match what I have always shown in my career.
But Ronaldo won't steal all the headlines from this particular game.
With his first brace in Serie A, Ronaldo has gained his 400th league goal making him only the fifth player in history to reach such milestone.
The player's actions were branded as unacceptable by Juventus head coach Massimiliano Allegri, with the club expected to issue internal sanctions. The second goal was brilliant. "But I am happy, I knew that I was working well and that the goals were going to come".
The Germany global also compared playing with Liverpool in the Premier League to playing in Italy. "It's a very hard group, we know that we can do well and Juve must focus on being the best".
Juventus have lifted Serie A for the past seven seasons though haven't won the Champions League since 1996.