Brunt received jeers from the crowd after being substituted during Albion's 2-0 home defeat on Saturday.
"It is absolutely ridiculous that somebody who has been an incredible servant to this club for such a long time gets that," The Guardian quotes Foster as saying. "He always gives his all and he's somebody I would always have in the team. It's not needed. It is really silly. It doesn't help at all. It's pathetic, to be honest.
"He is everything we're about. He works his socks off. There's no need to boo somebody. If he very obviously wasn't putting it in or couldn't be bothered, then fair enough, but that's not the case. Nobody likes that [being booed], I don't care who you are, whether you're the manager, the goalkeeper or centre-forward.
"If you're getting ridiculed and abused like that, it affects you and there's no need for it. These are our supporters and we need our supporters to support us and not do things like that. It's not nice. You can understand frustration but it's not like we're not trying. If that happens, fans are well within their rights to do whatever they like."
West Brom are yet to win a match in the Premier League this season, having drawn two and lost two of their first four games.