Carson was dismissed for violent conduct eight minutes from time after clashing with Bluebirds striker Michael Chopra.
- West Brom 0-2 Cardiff
The shot-stopper, who now faces a three-game ban, told Albion's official website: "I'm captain of the team, a role I take very seriously, and I shouldn't have reacted in the way I did.
"It was a really frustrating night and that came to the fore with my red card. A cross came over and I got caught by their player, who got nowhere near the ball.
"I should have just let it go and I'm disappointed in myself for getting involved. Having said that, I believe I was provoked and am disappointed in the way a fellow professional reacted.
"But I apologise to the players, the supporters and everyone connected with the club for the fact I was sent off and left us a man short."