The Brazilian winger, scorer of three goals in his first two Premier League appearances after joining from Watford, was dismissed shortly before half-time for making minor contact in a headbutt on Adam Smith.
Richarlison's reaction appeared to be sparked by comments from Smith that led to a heated exchange but Silva dismissed provocation as a possible excuse for the 21-year-old's actions.
"It is naive, it is something Richarlison cannot do," the Toffees boss said.
"It is something for the boy to learn fast, but it is something we can see many, many times in a football match.
"Both players to put their heads against one another and with minimum contact or movement as well. But it is something he cannot do.
"We have to keep our strong mentality every time, with a good emotional balance to support everything, whether an opponent provokes you or not, because the opponent is doing his job as well.
"It looks minimal, the contact. Of course, I respect the referee's decision as well. But it's something I don't like to see in my players and it's something you cannot do."
Everton overcame the setback to score twice either side of Smith's own 61st-minute dismissal for bringing down Theo Walcott before Bournemouth rallied to earn a draw courtesy of late goals from Joshua King and Nathan Ake.
The result marked a league-high 25th point the unbeaten Cherries have earned from losing positions since the start of last season but manager Eddie Howe urged his side to learn from repeatedly falling behind.
"It's certainly not our intent and certainly something we've got to solve in the sense of going behind and giving the initiative to the other team," Howe said.
"Against the top teams there's no way back, so it's certainly something we're going to have to improve.
"But we've done it again, we have got something out of the game which is really important... seven [points] out of nine, it's been a good start."