Howard, who played under Moyes during his time as Everton boss, believes that the 50-year-old is the right man for the job.
"I think this club will succeed and David Moyes, given the right time, will be a huge success. I think it is a very good combination," Howard told ESPN.
"People have too much time on their hands. Unfortunately that's what a lot of people do; talk and speculate. Manchester United, one of the biggest clubs in the world, gave him a six-year contract.
"Replacing Alex Ferguson wasn't going to be an easy thing; it's a monumental task, and I think everyone is well aware of that. Why people, whoever they are, talk is beyond me, but that's football."
Howard made 77 appearances for United between 2003 and 2007.