The 50-year-old, who took over when Alex Ferguson retired at the end of last season, has been astonished by the passion for the club both on the first stop of the tour in Thailand, where United lost, and in Sydney, where they won 5-1 on Saturday.
More than 20,000 turned out to watch the English champions train on Friday night and tickets for Saturday's match against an All Star XI picked from the local A-League sold out in eight minutes with 83,127 packed into the Olympic Stadium.
"It was a good game for us," Moyes said afterwards. "(But) more importantly to get 83,000 at the game - and I'd say all Manchester United supporters - is incredible and I thank all of them for coming to the game.
"It was a great night and a very special night to get my first victory as Manchester United manager."
With great support also comes great expectation and every day in the job makes it clearer and clearer just what a monumental task he faces to get anywhere close to his most hallowed predecessors - Matt Busby and Ferguson.
"The enormity of the job sunk even more yesterday when I saw an incredible video about Manchester United, seen Sir Matt Busby followed by Sir Alex Ferguson," he said on Friday.
"If I didn't know it before, I certainly knew it when I saw what those two gentlemen had done before me.
"It's a great job, it's a fantastic club - a football club that everybody in the world knows the name of and I'm very fortunate and privileged I was given the opportunity to manage.
"And I hope I can come as close to the success that the two gentlemen before me enjoyed."
Moyes's task over the six years of his contract is to ensure he is being bracketed with the two illustrious Scots and not with Wilf McGuinness, Frank O'Farrell, Tommy Docherty, Dave Sexton and Ron Atkinson, who were less successful in the job.
The former Everton manager also got an inkling this week of what kind of protection he can expect from the massed ranks of the Manchester United machine, represented in Sydney by nearly 200 club staff.
Australian reporters, who work in one of the most commercialized sporting environments in the world, were astonished by control exerted by the club in the few opportunities there were to talk to Moyes over the week.
At the post-match news conference on Saturday, the club official accompanying Moyes was trying to extract him from his chair pretty much as soon as he sat down.
As a result, the story of the rift with Wayne Rooney that threatens to end the England striker's time at the club bubbled all week without a meaningful contribution from Moyes - the man whose comments apparently caused it.
There was precious little more information on Moyes's transfer targets, particularly the attempt to wrest Barcelona midfielder Cesc Fabregas away from the Camp Nou.
"I've not had any more news," Moyes said on Saturday. "I have no more updates on anything really, so there is nothing positive or negative."
- Sports & Recreation
- Manchester United
- Alex Ferguson
- Matt Busby