The 31-year-old was sent for an early bath after lashing out in the direction of the German right-back, with the score at that point at only 1-0.
Steve Clarke's side were unable to find their way back into the game after going a man down, and Fulham eased to a comfortable win at Craven Cottage.
"It made things harder for my team," Odemwingie told reporters. "One man advantage is a big advantage.
"Hopefully when I come back playing I will compensate my team with some good actions and contributions to the next win.
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Odemwingie will now serve a three-match ban and promised to do his utmost to ensure that he would not be guilty of similar conduct in the future.
The 31-year-old did claim, however, that he felt the decision to send him off was a harsh one.
"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," he said.
"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."