De Rossi was sent off with his side leading 1-0 after 69 minutes for hitting Lapadula in the face and the Genoa striker scored the resulting penalty for a 1-1 Serie A draw.
“The first thing I did was slap him!” Di Francesco laughed at a press-conference before this weekend’s Serie A game against SPAL.
“Joking aside, like with a child you have to help them in times of difficulty. He’ll pay what he has to pay according to our internal rules, which will remain internal. Measures will be taken.
“After that everything will start from scratch. He, who is a real Romanista, has to feel supported in times of difficulty.”
The 34-year-old former Italy midfielder was punished for “seriously unsportsmanlike conduct”, meaning he will miss their next two league games against SPAL and Chievo.