The west Midlands club started the season in excellent form under new manager Steve Clarke, placing as high as third in the English Premier League.
But West Brom are without a win in their past four league games, losing three on the bounce, and Odemwingie has attributed the run to more negative tactics from rival teams.
“They’ve seen we have quality and pace. I’ve noticed people play more carefully against us now,” Odemwingie told BBC WM.
“It becomes a bit more difficult but that’s when you need to show character and belief that we are growing.
“We have been doing well this season and we’ve had a bad three weeks but hopefully we can score goals again.”
Odemwingie is likely to take part in the Africa Cup of Nations with Nigeria but believes the squad will cope admirably in his absence.
“I want to be going there in the New Year with West Brom high in the table, which would help me emotionally,” he said.
“Of course I will miss a couple of weeks of action here but I believe we have a squad that can hold on to the good start we have had.”