West Brom have not won a match since Pepe Mel replaced Steve Clarke as head coach of the midlands club.
"I'd be very surprised if Pepe Mel is under pressure at this moment," he said.
"I wouldn't think for one minute that after six games they were (thinking about) bringing in a new manager."
Moyes admits he was surprised to see his Clarke sacked.
"I'm not privy to what goes on at West Brom but I thought he did a great job last year and had them in a lofty position in the Premier League," Moyes added.
"When I was at Everton last year, they were challenging us a lot of the time and he did really well so I'm surprised Steve left.
"I'm not aware what has gone on at West Brom but he's a good manager and proved that in his time at West Brom."
For breaking stories and all the great banter like us on Facebook: facebook.com/tribalfootball