The Serbia international marked his return to the top flight with a brace in a 2-2 draw against Liverpool.
Mitrovic has long been seen as a player who is too good for the Championship but out of his depth in the Premier League.
Now, Silva has backed his star forward to change that perception, saying: "He is a Premier League striker. He has competed in the Premier League. In the last seven seasons he has played four in the Premier League.
"That means he's a Premier League striker, otherwise he would not be here with us.
"That's the main thing. He's a Premier League striker, he's the best scorer of his national team, he's a player with experience to play the most difficult competitions in the world with his national team.
"I don't have doubts. From last season, now I don't need to see Mitro scoring goals at this level to say that he's definitely a Premier League striker.
"Of course you have to understand his profile and take the best from him. It is my job to do that and keep providing for him and delivering for him.
"For sure he can finish, but he is more than that for me. He's a football player, a striker who can add something different. With the ball, without the ball, he is working really hard.
"I am really pleased to see him involved in our defensive process as well and I expect more from him, to be honest.
"He has more to give us, and to keep playing with a smile on his face is what I want to see. In some moments he will not be perfect, but he was almost perfect against Liverpool."