Star-man Richarlison was shown a straight red card just before half time, but Everton took the initiative and earned a two goal lead. However, they could not hold on, as Joshua King and Nathan Ake scored within a hectic five-minute period to earn a point for Bournemouth.
In the post-match interview Silva was quoted by Sky Sports voicing his opinion towards Richarlison's sending off, saying: "Until that moment, a balanced game. We knew before the match it would be a tough game for us, but we came here to make the game tough for our opponent as well.
"To be clear, it is something our players cannot do, even Richarlison. We have to keep our strong mentality every time, to be with a good emotional balance every time to support everything."
"It looks minimal, the contact. Of course I respect the decision of the referee as well, but it is something I don't like to see in my players, and is something you cannot do."
Richarlison appeared to be provoked by Bournemouth's Adam Smith, and Silva stated that he also believed that Smith had instigated the contact, remarking: "I think, yes. It's naive, it's something Richarlison cannot do.
"It's something for him to learn fast, but it is something we can see many, many times in one football match, both players to put their heads against each other with minimal contact.
"But I repeat again, it is something he cannot do."
When asked about his opinion of Everton's overall performance, Silva was quick to praise his side's performance in the second half. He said: "Yes, we did amazing. I asked them to keep our shape and organisation, but never give up and believe always that you can score. Our first goal is a fantastic example, and after we had a fantastic chance with a free kick to score a second.
"It is not easy to play in three games, twice with ten players. Again, they did fantastic work until that moment. We lost our balance, it's not the moment to concede a penalty but we did. After, of course they are believing, and from a corner they score the second goal.
"It's tough for us, because our players deserve something more. But it's football, it's something for us to learn as well."
Everton will have to get used to playing without their star goal-scorer for a while, leaving the field open for the rest of the forwards who will get their chance as soon as Wednesday, when Everton hosts Rotherham in the second round of the FL Cup.