"I think it's the hardest start for 20 years that Manchester United have had," Moyes told the BBC on Thursday.
"I hope it's not because Manchester United won the league quite comfortably last year (that) the fixtures have been made much more difficult.
"I find it hard to believe that's the way the balls came out of the bag, that's for sure," added Moyes ahead of his team's first match at Swansea City on Saturday.
The game with United is the only meeting title rivals Manchester City have with a top-five opponent from last season in their opening five fixtures.
Chelsea also face only one other game against a top-five opponent in that spell, at United on August 26.
Former Everton boss Moyes took over at Manchester United in the close season following Alex Ferguson's retirement.
(Reporting by Josh Reich; editing by Tony Jimenez)
