United suffered a 4-1 defeat at the hands of rivals Manchester City at the Etihad Stadium on Sunday, with Sergio Aguero netting a double for the hosts, while Yaya Toure and Samir Nasri also found the net.
The result means that Moyes has now slipped to defeat in both of United's traditional derby matches so far this season, with the disappointment at City following a 1-0 loss at Liverpool earlier in the month.
The defending Premier League champions have taken just seven points from five games this term, but Moyes - who took over following the end of Alex Ferguson's 27-year spell at the helm - believes their early struggles should not come as a shock.
"I think any manager who'd been given that run of fixtures when they took over at the club would have found it difficult," he said.
Moyes also expressed frustration over the poor performances against City and Liverpool, but is hopeful better results will come as he becomes more familiar with his players.
"We want to win more of those games, we have to do that," he added.
"But maybe if those games are later in the season and not right at the early part of it then I might have a better understanding of all the players, the situation at the club."
United are set to face Liverpool again on Wednesday, when the sides meet in the League Cup at Old Trafford.
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