Moyes has experienced a mixed start to life at United having missed out on a number of targets in the transfer window but won both of his opening two competitive games in charge.
The former Everton manager's biggest test yet comes this evening when his side host Chelsea, and he acknowledged that he would have to earn the fans' support and hopes that the transitional period will be a smooth one for the club.
"I won't be taking that support for granted. I know I have to earn it. I know I have to go out there and show you fans, and everyone at Manchester United, that I'm the right successor," Moyes wrote in his programme notes for tonight's game.
"There is no doubt we are in a transitional period at the club - most people recognise that when a new manager joins - but I'm hoping that it's going to go smoothly and there won't be too many bumps along the way."
United yesterday confirmed that they had sold a record 63,000 season tickets for the current season.