And he offered a message to “remember where your place is” amid his backing of his opposite number.
Speaking in what was generally a light-hearted press conference, the Everton boss was happy to give Hurzeler praise when asked.
Told his opposite number was unpopular with some supporters, he said: "I am nearly going 'you're joking' with my mouth ajar. Are you having a laugh?
“He is doing unbelievable. He is doing a brilliant, brilliant job for Brighton.
“You should consider yourselves incredibly lucky to have such a manager.”
With possible reference to West Ham, Moyes said: “I've been in a couple of places recently where sometimes the grass isn't always greener.
"It's an incredibly well run club with good ideas. Sometimes you have just got to remember where your place is.
"You might have a manager who goes on to manage the German national team in years to come. You have certainly got someone with big prospects."
Moyes complained about the yellow card he received for dancing on the pitch after Beto scored his late equaliser.
He said: “We’re killing it that the managers can’t come out of their technical area to celebrate a goal, knee sliding, do things which give you people quite a bit to talk about.”
Asked if he would do it again, Moyes replied: “I bloody will do it again!
“Actually, if I’d been a bit more mobile, I might have done a knee slide. That would only have got me a yellow as well, so I might as well have gone the whole hog.”