The Brazil defender was dismissed for his high tackle on Sead Kolasinac late in the goalless draw at Stamford Bridge.
Wilkins told talkSPORT: “It was an atrocious tackle. He either wants to hurt Kolasinac, or he's afraid. I'll go for the latter.
"He saw him coming towards him and thought: 'Wow, this fella is a giant' and he basically wet himself.
“Kolasinac went to the floor, his boots never came off the ground, he just went for the ball.
"If Luiz had done that there would have been nothing wrong. It's on the halfway line for goodness sake."