After a lethargic display in last weekend’s pre-season opener in Bangkok, United looked slick at the ANZ Stadium, comfortably overcoming the hosts in front of 83,000 fans.
"It was a special night to get my first victory as Manchester United manager," he told a press conference. "It was a good performance. We could maybe have got a few more goals – we hit the post and had one or two other chances as well.
"The opposition put on a good show, especially in the first half, when they caused us one or two problems. Once we got the goals we got the chance to control the game a little.
"It was a good game for us. We stepped up and I thought we looked a bit fitter tonight, a bit more ready, and the temperature possibly helped us a bit more than in Thailand."
Jesse Lingard and Danny Welbeck scored two apiece before, in his first pre-season action, Robin van Persie netted a fifth, and Moyes had praise for them all.
"To get Robin back on and started was good but I think it was impressive that Danny scored a couple of goals – he might have got four or five on another night," Moyes said.
"The keeper saved one from him with his feet in the first half and he was a bit unlucky. He made a couple of great runs.
"Jesse played well and I was hoping he would get a hat-trick because I think for a young boy to do that for Manchester United is a big thing.