Pardew was at a loss to explain referee Mike Dean's lenience with Luiz, and was not convinced by the answer he got when he spoke to the official at the break.
He said: "I thought he was going to be sent off. It was the fourth minute of the game, but it doesn't really matter when that moment arrives.
"He [Ba] was in on goal, he was in behind Luiz, the goalie was not going to get to the ball, therefore it's a goalscoring opportunity, and he brought him down.
"I couldn't quite understand why he didn't send him off. I was really angry about it because if that had happened at Old Trafford with one of my players, one of my players would have walked, and I thought he would have walked today.
"The referee said to me at half-time that he [Ba] didn't have control of the ball.
"I am not quite sure of the rule book, so I need to get that out and have a look at it."
Villas-Boas, who confirmed that transfer requests from Alex and Nicolas Anelka had been accepted, admitted Luiz might have been fortunate, but was full of praise for his players.
He said: "They were amazing and show fantastic team and fighting spirits when everything is against them, when they are in the newspapers being questioned.
"We don't know why because we have full belief in them and today, it was a much-deserved win for them and the praise should be shared by all of them."