Dowie believes Everton should be a model for other clubs.
"I'm a huge admirer of David Moyes and he's certainly got the best out of his players," Dowie told evertonfc.com.
"I think he's up there amongst the top three or four managers in the Premier League - I've always believed that.
"He's coped with everything really well. He's just got on with what him and Steve Round do really well.
"Bill Kenwright knows he's got a very good manager there and he knows that David Moyes will work the players hard and get the best out of them.
"As a chairman that's what you want from your manager - that you do it in the right way and David Moyes has always done that."