The two sides will lock horns twice in the space of five days, firstly in the Premier League at Villa Park on Tuesday before resuming hostilities at the same venue in the FA Cup on Saturday.
Villa languish second from bottom in the league, adrift of safety on goal difference after 12 matches without a win, while West Brom are eight points better off.
At the forefront of Brunt's mind is Tuesday's fixture, where West Brom will seek to make it five league games unbeaten.
"Obviously Villa are having a bad time at the moment and they are not scoring many goals, but that run has to come to an end at some stage and it's important that we make sure it's not against us," Brunt said.
"I hope we can use the pressure on them to our advantage, but it's a local derby and form usually goes out the window.
"We saw that last season when Villa hadn't been scoring many goals, we hadn't scored many either and we ended up sharing seven in 90 minutes.
"With the way results went for us on Saturday, we will go there aiming to extend our unbeaten run. It's going to be a difficult game for us – but it will be difficult for them as well.
"There is pride at stake in the area, but we have to block that out. The Cup game will be special when we get to it, but it's important that we concentrate on the League game first.
"Then we can turn our attention to the FA Cup – and one way or another it will be a big week for people in the Midlands."
Last season's match at Villa Park finished 4-3 to the hosts.
