Boss Sam Allardyce criticised Jake Livermore and hinted he could lose the West Brom captaincy after his red card in Albion's nightmare derby defeat.
Livermore was shown a first-half red card, after a VAR review, for a lunge on Jack Grealish to compound Allardyce's woes in his first game in charge.
It was the Baggies' third red of the season and he will miss the next three games, with Allardyce refusing to rule out a change of captaincy.
"It depends who wants to be captain after this and who can handle the armband. If I consider they are good enough they can keep it," said the former England manager, with Albion second bottom in the Premier League.
"I won't accept another sending-off, no matter what. We have to stop that otherwise we won't have a chance of getting out of this trouble.
"It's the first thing I asked the players do to, whatever you do don't get sent off. I'm upset, I couldn't be anything else but upset.
"He has apologised to the players and to us. He looks very upset about it but from my point of view an experienced player like him should not have put himself in that position.
"We have to deal with it and it means we not only suffer today but also because we can't pick him for three games. We need every player we have got who has Premier League experience. We haven't got many of those.
"The 10 men battled bravely to try to stay in the game. They tried and tried against a Villa side who are playing very well this season.
"I'm really disappointed with the result but do give the 10 men credit for sticking to their task."
El Ghazi opened the scoring after five minutes when he converted Traore's cross from close range.
Albion never recovered and their hopes were over eight minutes before the break when Livermore was dismissed for a dangerous challenge on Grealish.
Referee Martin Atkinson initially gave the midfielder a yellow card but upgraded it to a red after viewing his pitchside monitor.
Soon after Kortney Hause was cautioned for catching Grady Diangana on his ankle, with Albion questioning why the defender was not also sent off.
Ollie Watkins had a goal ruled out for offside but Villa made the game safe with six minutes left when Traore coolly found the bottom corner from the edge of the box.
It was 3-0 two minutes from time when El Ghazi scored from the spot after Semi Ajayi's clumsy foul on Grealish.
Villa are now just three points off the top five with two games in hand after back-to-back away derby victories following last week's win at Wolves.
"With the pandemic I am not thinking about Europe at all as we can't travel at the moment," smiled boss Dean Smith.
"But, seriously, we are not thinking of it at all. We are just thinking of the next game.
"There is a great focus at the moment and there is a willingness to keep progressing as a club and as individual players.
"As long as I have got that, whatever will be will be. We will just keep working hard.
"It was an excellent performance. We wanted to negate the new manager bounce teams can have and I thought we did that really well.
"We got a great goal to start with and restricted them, I can't remember their chances such was our control of the game."