As he prepares to return to Fluminense this summer, the 39 year-old told Sky Sports: "Thiago knows what it means to wear a Chelsea shirt, you know.
"And if I have a message to send to the boys that are here today, I hope they understand that everything they did to get to Chelsea has to be worth it.
"Because the season we're having is not worthy of Chelsea. It's not.
"And I think they have to do more next year, they need to do more."
Silva also said of Chelsea supporters: "If you look at the games, the fans never left the team, never.
"We were in ninth place, eighth, right? And the fans were always there.
"They booed us off a little at the end of the match, but they're always there in the stands, always with 40,000, 45,000.
"If we were somewhere else, they could throw rocks at us - we know that happens in our country.
"So these boys need to be aware that Chelsea has to fight for the top positions.
"If we take a little of our ego and put it in favour of the team, I think it will work. If we don't do that, the situation will hardly change unfortunately."