United landed in Sydney on Sunday afternoon, the second leg of this season's summer tour and the first without Sir Alex Ferguson in 26 years.
Moyes' first exposure to a United pre-season came in Bangkok last week, where the Reds spent three nights in the Thailand capital amid fevered interest from the locals.
Moyes visited Australia with Everton in 2011 but the new United manager admits the level of interest his former side generated is nothing compared to the Reds' pulling power.
"I managed a very good club at Everton and we had great support out here – we visited Sydney, Melbourne and Brisbane and enjoyed that – but I have to put this into perspective and it's completely different," he said.
"The amount of support we've had, the amount of interest from the press... we're constantly watched and scrutinised and it's something I'll have to come to terms with.
"But the previous manager, Sir Alex, told me what to expect. He told me especially what the tours were going to be like and I think if you have a football club like Manchester United you have to make sure you go to your supporters worldwide and I think as a football club Manchester United do that very well.
"They take the club around the world and try and engage with the supporters wherever they are."
Moyes' first game in charge – a 1-0 defeat to a Singha All Star XI in Thailand on