The Baggies were able to stop the rot which saw them lose three consecutive matches by drawing with the visiting Hammers and although it wasn't a great performance, Brunt felt the defensive showing was pleasing.
"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," he told Sky Sports.
"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."