Fulham had Raul Jimenez sent off in the 22nd minute for an aerial lunge on Sean Longstaff after the Mexican striker hit the Newcastle midfielder in the face with his hip as he attempted to block a pass.
Although the red card came after a VAR review, Silva said Barrott had failed to punish Jamaal Lascelles for an elbow on Jimenez, which caused the Mexican forward to lose his cool and commit the foul which led to his dismissal.
"Until the 21st minute, all the moments, the referee didn't give us one foul. For Newcastle it was a free kick every time," Marco Silva told BBC Sport.
Silva insisted that the Premier League needed to pick referees with the experience and ability to cope with big games.
"This is the best example of a referee who doesn't have the experience to handle the pressure. Any doubt, any foul, he didn't give one. Even the elbow in the face of Raul."
Silva said the referee's initial decision to caution Jimenez was right and blamed VAR for interfering, with Barrott overturning his yellow card for a red after watching replays.
"He jumped into the player but you don't see something serious, something wrong with the other player. A yellow is right," he added.
"VAR is trying to find all these moments to give. To justify their job? I don't know. It's clear he (Jimenez) lost the momentum. He should have done it in a different way.
"To go for a red card feels really strange. It was a strange afternoon for the referee. I went to speak with him but he almost ran to the dressing room. It's what we're facing right now."
