The London club are smarting after Carroll was given a three-match ban following a clash with the Swansea defender last week, with many thinking Chico made the most of whatever contact there was.
United vice-chairman Brady certainly subscribes to the view that Chico was guilty of play-acting.
She told the Sun in her weekly diary: "Andy Carroll is red-carded for what amounts to accidentally distrubing the ponytail of an opponent.
"Swansea's Chico Flores clutches his face and rolls around bodypopping on the floor like he's been shot. It's one of the worst cases of bad sportsmanship I have seen in 20 years."
West Ham failed in two appeals to have Carroll's ban overturned and Brady is unhappy that while her man has to sit out, Chico can carry on playing.
"Swansea can pick Chico Flores who pretended that he had suffered what appeared to be at least brain damage when his ponytail got 'air' brushed by Andy's arm," she added.
"I had brain surgery in 2006 and even then I didn't roll around four times."