The Brazil international did not feature in the matchday squad for the 1-0 win at Stamford Bridge.
Andreas Christensen, who took Luiz's place, impressed in the centre of defence as Manchester United striker Romelu Lukaku struggled to get the better of the Denmark international.
Wilkins, who played for Chelsea and spent numerous spells as their assistant coach, believes Luiz is too much of a liability in defence and thinks he would be better suited to a midfield role.
He told 'Sky Sports': "He's not been playing well. He's lackadaisical as a defender but I think he is a very good midfield player and I have said this on numerous occasions.
"Christensen came in yesterday and played very, very well indeed in a massive game.
"How many times do you see Christensen in advance of the ball? You don't, because he thinks defensively.
"With Luiz you see him in advance of the ball on numerous occasions during every game he plays and consequently, Chelsea suffer defensively.
"I thought the decision to drop Luiz was the right decision. I saw him play against Roma [a 3-0 Champions League defeat] the other night and he didn't look anywhere near it. That was a poor performance.
"Yesterday was one of effervescence, they had life, and I thought Chelsea deserved to win."