The Baggies ended a run of three successive defeats against the Hammers on Sunday, but were forced to settle for a share of the spoils in a goalless draw.
Steve Clarke's side will be concerned at having gone three games without troubling the scorers, but club captain Brunt believes they are heading in the right direction.
He told Sky Sports: "I think we were a bit sloppy in the first half. In the second half we put them under a lot of pressure but couldn't break through.
"To be fair they defended pretty well and at certain points we did come close to getting a result. A point takes us off that losing streak we were on.
"(A clean sheet is) very welcome. We haven't had too many recently so credit to the back four and Boaz (Myhill) as well. He's come in (for the injured Ben Foster) and done very well having been on the wrong side of a few bad results.
"It's a good clean sheet and a good point but I think we were a bit disappointed not to take all three in the end."
A stalemate on home soil prevented West Brom from closing on the top four, but one of this season's surprise packages have still taken 27 points from 17 games - and Brunt is more than happy with that return.
"At the start of the season we would have snapped somebody's hand off for it but I think we should be kicking on," he added.
"But it was important to get something today and hopefully that can help us going into the Christmas period."
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