Evans made the comments about the Italian following the Whites’ 1-0 victory over Preston North End at Elland Road on Sunday afternoon.
Silvestri started the Championship game and played for the entire 90 minutes, making as many as nine saves.
Evans was impressed with the display of the 24-year-old, who has made errors on occasions this season.
“I can’t speak highly enough of him,” the Scot told The Yorkshire Evening Post about Silvestri. “He’s a top-class goalkeeper and I’m glad that he’s demonstrating that because it’s easy for people to say it. It’s harder to go out, demonstrate it and prove a point than it is to talk.”
Over the course of the 90 minutes at Elland Road, hosts Leeds had 59% of the possession, took 12 shots of which just two were on target, and earned eight corners.
Visitors Preston, who finished the game with 10 men, had 41% of the possession, took nine shots of which seven were on target, and earned five corners.
Leeds are 13th in the Championship table at the moment with 29 points from 22 matches, just five points behind Ipswich Town, who are currently sixth and occupy the final playoff spot.
The West Yorkshire outfit will return to action this coming Sunday when they take on Nottingham Forest away from home at the City Ground.
Forest are currently 15th in the standings with 28 points from 22 matches.