Giggs is about to begin his 23rd season as a United player, but his first with Moyes as manager of the side rather than Sir Alex Ferguson.
However, having arrived in Sydney for the second leg of United's tour, the Welshman says he remains as enthusiastic as ever.
"I've only had one manager for 20 years, so it's strange, but you move on," said Giggs.
"I've really enjoyed it. Just like any other pre-season, you've got to work hard, knuckle down and prepare yourself as best you can for the first (Premier League) game of the season against Swansea.
"Crazy, aren't I? I'm enjoying it just as much as I did 20 years ago. It's as simple as that.
"Every year is a bonus to me. Take last year, when we won the league. Winning that trophy makes it all worthwhile, and that feeling you have after the hard work you put in.
"The thing about Manchester United is you have to do it all over again. This is the start of the journey this season and I hope to be lifting a trophy again at the end of it.
"We have to put the hard work in now, in order to achieve that."
We are under constant scrutiny
Moyes also spoke to the press in Sydney and admitted that he is still coming to terms with the amount of attention he is now receiving.
"I have to put this in perspective and it is completely different," said Moyes.
"The amount of support we've had, the amount of interest we've had from you people (the media), constantly we are watched and scrutinised, and it's something I'll need to come to terms with.
"I'm following probably the finest football manager that's ever lived. I'm always saying if I can even win a quarter of what he won, I'll have done very well.
"But the first thing I've got to do is settle into the job, get to know everybody, and find my way around."