The winger had been involved in a number of challenges with Cherries right back Adam Smith throughout proceedings.
That came to the boil in the 41 minute, with the Everton man upset with something the defender had said or done.
The two squared up to each other before Richarlison leant his head into the Bournemouth man, with Smith reacting and the Everton star being sent off.
Silva told the Liverpool Echo: “To be clear, it's [the red card] something Richarlison or the other players in our squad cannot do.
“It's something I don't like to see, and at this level even if you're 18, 19, 20, 33 you have to keep your emotional balance there, keep your mentality as well.
“If someone provokes you or not, if the fans are against you or not you have to keep that.
“It looks minimum the contact, I'm not one to talk about the referee's decision.
“What I can tell you is about my players and I don't like them to do that."