Barrios appeared to move his head into Jordan Henderson’s chest and then quickly move his head up onto the England star’s chin in the first half.
However, Barrios was only given a yellow card despite the use of the Video Assistant Referee.
Clattenburg says the first contact was only a yellow but claims the movement up was violent conduct and a red card should have been brandished.
“Clearly England are not getting any justice with the VAR system,” he said on ITV.
“What you can see from this footage is that the defender has put his head into Jordan Henderson’s chest, therefore I think this is a yellow card.
“But what I then do see is the movement up with his head and that is clearly violent conduct because he know what he’s doing and this is a pre-meditated act.”
Clattenburg says the VAR should have told the on-field referee to review the incident on the side of the pitch.
“The referee’s on the pitch, he’s got the temperature, the feeling,” he added.
“You can see in the first half it’s a very spiky game.
“He knows the feeling on the pitch.
“What I would rather see is the video referee, instead of giving his opinion which is a yellow card, I would rather see the referee go to the review area and make the correct call, which is a red card for violent conduct.”
The game ended 1-1 at the end of normal time, with Yerry Mina’s header cancelling out Harry Kane’s opener.