Alan Irvine's side failed to secure their first Premier League win when they were beaten 2-0 by Everton at The Hawthorns at the weekend.
Some Albion fans directed their frustration at long-serving midfielder Brunt and England goalkeeper Foster was baffled to hear the Northern Ireland international targeted.
"If you’re getting ridiculed and abused like that it affects you and there's no need for it," Foster said.
"It is really silly. It doesn't help at all. It's pathetic, to be honest. These are our supporters and we need our supporters to support us and not do things like that.
"It's not nice. It is absolutely ridiculous that somebody who has been an incredible servant to this club for such a long time gets that.
"We're four games in. We're not even thinking about pressure. We are definitely a much better team than last season but it’s just not going for us at the minute."
Albion face a trip to Tottenham in their next top-flight game on Sunday.
