King had a difficult time in his first few games, with a goal being disallowed against Chelsea and a mistake leading to a goal against Brentford. This has led to concerns about the 18-year-old's performance.
However, Silva has praised King's reaction to these setbacks, saying he was pleased with how the young player responded.
"I was very pleased with the way he reacted," Silva said ahead of Fulham's Carabao Cup tie with Cambridge.
"Even after a difficult moment, like the mistake he made, it's normal to have a bad moment, but the way he reacted pleased me a lot. It's not easy to bounce back from a mistake like that, but King's response was very good."
Silva trusts King, who has started all five of Fulham's Premier League games this season, and believes the teenager has shown maturity beyond his years.
"It's nice to see a young player like King, who is 18, show composure and maturity in tough situations. He's doing well and I'm pleased with his progress."