Odemwingie had the chance to put the Baggies 2-1 ahead against United only to miss the target with the Baggies going on to lose the game 2-1.
Brunt, although a little perturbed at being overlooked for the penalty, believes Odemwingie will bounce back very soon.
“I hope I get a chance to take a penalty again. I missed one earlier in the season against Arsenal and got booted off them,” he told the club’s official website.
“Peter scored the penalty at West Ham and when he put the ball on the spot and we were all pretty confident he would score.
“He’s going through one of those spells at the moment when nothing seems to be going right for him in front of goal.
“I’m sure that will turn as long as he keeps working at it. He’s done very well this season so we won’t hold that against him.”
West Brom outplayed United for long periods of Saturday’s game but they could not make their pressure tell, much to the annoyance of Brunt who believes the game was there to be won.
He said: “There wasn’t much more we could have done to try and win the game. That’s been the general feeling over the Christmas period.”
“We’ve created a lot of chances and shot ourselves in the foot by giving away sloppy goals.
“It was the same today and you can’t give teams like Manchester United goals from set-pieces and goals after two minutes into the game.
“We let ourselves down with that – but we created a lot of chances but we didn’t take them.”