The west Midlands club started the season in excellent form under new manager Steve Clarke, placing as high as third in the table.
But the Baggies are without a win in their last four league games, losing three on the bounce, and Odemwingie has attributed the run to more negative tactics from rival teams.
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|15/2||Peter Odemwingie is 15/2 with William Hill to score first in a West Brom win over Norwich City
"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 that 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," the striker added.
"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."