The Nigeria international was dismissed in the first-half for kicking out at Fulham defender Sascha Riether as the Baggies slumped to their first defeat of the season.
"If I didn't get kicked first that wouldn't have happened. Still can't understand why I reacted like that today. Normal to get kicked,” Odemwingie took to his Twitter feed to explain.
"It made things harder for my team. One man advantage is a big advantage," he later added in an interview.
"Hopefully when I come back playing I will compensate my team with some good actions and contributions to the next win.
"As a team we need to bounce back. We are a united group and I had encouragement from my team-mates to forget about it. I will be more worried if it happened more often than one or two times in my career."
And the 31-year-old former Lokomotiv Moscow striker also insisted he will not let the red mist descend in the future, even if he feels he has been hard done by.
He said: "It is something I will learn and hopefully it won't repeat itself and next time I play in an important game for the club, I hope I remember this even if someone provokes me or not.
"I'll try to keep my cool and not react. I feel it was too harsh. I didn't lead with my studs, I just wanted to foul because I felt there was a foul against me that wasn't noticed when I wasn't far from the linesman.
"That moment happens, it doesn't happen often, but for some reason I lost my temper and I regret it. Now I'm thinking about bouncing back for my team."