Mitrovic took his seasonal tally to six, taking him up to second in the Sky Bet Championship scoring charts.
But his manager was eager to stress that there is a lot more to the striker's game than putting the ball in the net.
"I know Mitrovic and he's a very important player for us, not just because he scores goals. The way we use him to link our game and to break the pressure and find our midfielders around him," said Silva.
"He scored from the penalty in the first half and the second goal he scored was really important after 83 minutes, seeing him press the central defender to win the ball.
"I was really pleased to see that, showing to me that he's really involved in the team, not just scoring goals but pressing the opposition and all his work without the ball."
Nathaniel Chalobah made his debut for Fulham following his deadline-day move from Watford and the midfielder won the penalty and set up the third goal for Harry Wilson.
"He will be a really important player for us. Chalobah was a free and he is a fantastic signing for us and a fantastic opportunity, the quality he has," said Silva.
The result sent Fulham back to the top of the Sky Bet Championship table, with Denis Odoi's 10th-minute header opening the scoring and Mitrovic's 44th-minute penalty doubling Fulham's advantage.
Birmingham captain Harlee Dean's push on Chalobah won the spot-kick and then his second-half pass set up Wilson for the night's third goal.
Mitrovic added his second after a nice one-two with Jean Michael Seri before Troy Deeney's late consolation.
Birmingham manager Lee Bowyer felt the "difference in quality in the final third" was the decisive factor as his side fell to a first league defeat in four outings.
"Fulham were more clinical and had more quality than us in the final third, but I can't fault my players for their work-rate, hunger, passion and fight. They kept going to the end when they could have easily rolled over," said the Blues boss.
"We kept going and going and created chance after chance in the second half. It could have been a 4-4 game, I think. We lost 4-1 at home and just got clapped off by our own fans, so our fans recognise that we don't deserve that result."
Boyhood Blues fan Deeney scored his first Birmingham goal and went close on several other occasions from open play, despite only playing the final 37 minutes as a substitute.
"Troy deserved his goal. It was a proud moment and he'll go home happy that he's done something that he's wanted to do from a young age," said Bowyer.
"He brings a threat, whether he's going start or from the bench."