The Brazilian had a Premier League debut to forget as his heavy touch allowed Callum Robinson to score Albion's second goal of the game.
Writing on Instagram, Silva said: "There are days when unfortunately hard work doesn't pay off the way we expected.
"I am upset, but I take responsibility for the mistake I made, as I always did. As difficult as it may be, we have to get over this and move on.
"I want to thank my teammates and the entire staff for their continuous support since I joined Chelsea FC. I am really grateful of that support.
"I promise to all of you that I will give everything I have on the pitch, putting all my energy and commitment into the games to come."