“I lost my temper. I'm a professional and should have kept my cool, but it happens”
Peter OdemwingieWest Brom striker
The Nigerian international, 31, was dismissed as the Baggies trailed 1-0 in the first half at Craven Cottage.
"I wanted to foul the player because I thought he was angry towards me. But I should cool my emotions," he admitted.
"I've said sorry to the players and to the staff. It's a lesson to learn."
Fulham were leading through home debutant Dimitar Berbatov's strike when Odemwingie, restored to Albion's starting XI for the Premier League encounter, swung wildly at Riether from behind after losing possession to the German defender.
Referee Roger East instantly showed the red card following the 37th-minute incident.
Berbatov's penalty in first-half injury-time and Steve Sidwell's late finish then condemned Albion to their first defeat of the season.
WBA started too slowly - Clarke
"I am looking at the incident in a different way now," Odemwingie said. "That moment went very fast for me, I felt a kick on my ankle and felt an injustice that the linesman was so close but nothing was given.
"But now I think it was my fault. I lost my temper. I'm a professional and should have kept my cool, but it happens. It's not my habit."
Afterwards, Albion boss Steve Clarke refused to publicly criticise his player and vowed to quickly move on from the incident.
"We're all human - we have emotions," said the Scot. "Peter felt he had been fouled, felt it was a free-kick and reacted in the wrong way. The red card is there and he has accepted the punishment, we all have to accept it and move on."
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