Mel has yet to win since taking charge of the Premier League club in January, and West Brom have dropped from 14th in the table to 17th with only goal difference keeping them out of the relegation zone.
The 51-year-old has only collected four points from his seven games in charge, and talk of his possible departure has increased in the wake of Saturday's 3-0 defeat to Manchester United.
However, Foster believes that rumours of Mel going the same way as Steve Clarke and leaving the Hawthorns are unfounded.
"It's incredible (the speculation) isn't it?" the 30-year-old said. "But that's the way the game has gone. It's gone mad, completely crazy.
"It seems now that every new manager that comes in – unless they start winning straight away – is going to be in trouble.
"The players don't pay attention to the speculation about Pepe.
"I really like him, I think most of the guys do.
"I'm still confident we will be alright because we don't have any fancy Dans or individuals in this team.
"When it comes to the nitty-gritty we've got lads who are prepared to roll their sleeves up."
West Brom have only won twice in their last 22 league matches as their top-flight status has come under threat with 10 games remaining.
