Moyes succeeded the retired Sir Alex Ferguson at United over the summer and has seen his side pick up just seven points from their five Barclays Premier League games so far, suffering two losses along the way.
The champions' latest defeat came last Sunday in humiliating circumstances as they were thrashed 4-1 by derby rivals Manchester City at the Etihad Stadium.
They head into their next league game, Saturday's Old Trafford clash with Albion, off the back off a victory, though, having responded to the City debacle by beating Liverpool 1-0 at home in the Capital One Cup on Wednesday.
United also won their Champions League opener 4-2 against Bayer Leverkusen last week and, while Clarke believes it is natural there is a certain level of strain that comes with taking on the job of United boss, he has also questioned how bad things really are right now for ex-Everton manager Moyes.
"I'm sure David is feeling the pressure of being at a big club like Manchester United, even after 11 years at Everton, where he became established as a really good top-flight manager," Clarke said of his fellow 50-year-old Scot.
"The step up to a club like Manchester United, which is not only a football club but an institution, is big.
"I'm not so sure things haven't gone that well.
"They had a good win in midweek, so they have already bounced back from the City reverse.
"That's what the top teams do - they know how to recover from bad defeats."
He added: "David's work at Everton put him in a position where he deserved to be considered for the job.
"I can't see too many negatives to being manager of Manchester United.
"I think anybody with any sort of ambition would want to be the manager of a team of the stature of Manchester United."
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