"We've got a massive game against Scunthorpe, we've got to make sure the intensity and performance is there," said Mowbray.
"It's not just about turning up and winning. Scunthorpe are fighting for their lives, and will be giving it everything they've got."
The victory over the Robins was inspired by man-of-the moment Roman Bednar, who has hit seven goals in as many games.
He was replaced by on-loan Ishmael Miller with 20 minutes to go in that match, but Mowbray revealed it was just to keep him fresh for the rest of the festive period.
"I just saw signs of him blowing hard late on, having worked hard for 70 minutes," he explained.
"Roman has played a lot of games in a short space of time through necessity, without having played any football for a long time.
"He's got a lot of competition for a place, but he's stepped upto the plate when Miller and Kevin Phillips were out injured."
Unfortunately for the Iron, but Miller and Phillips are now back to full fitness - giving the Baggies an impressive array of free-scoring attackers.
Phillips made his first start following a knee cartilage problem on Boxing Day - and responded by hitting a brace, his 12th and 13th goals of the campaign.