The Baggies have not won in four Premier League matches, with three of those defeats, to fall to seventh place on the table after a brilliant start to the campaign.
Odemwingie believes that the negative results being produced by he and his teammates are down to opposition sides taking a much more defensive approach.
"They've seen we have quality and pace. I've noticed people play more careful against us now," Odemwingie told BBC West Midlands.
"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."
Albion will be looking to bounce back from their four-game winless streak when they host Norwich City, unbeaten in 10 league matches, on Saturday.