Moyes' first league game as United boss comes at Swansea on Saturday evening and they follow that up with a home game against Chelsea before away trips to Liverpool and Manchester City, either side of a visit to Old Trafford from newly-promoted Crystal Palace.
An aggrieved Moyes questioned such a run of fixtures and in quotes reported on the BBC Sport website, he said: "I think it's the hardest start for 20 years that Manchester United have had.
"I hope it's not because Manchester United won the league quite comfortably last year (that) the fixtures have been made much more difficult."
He added: "I find it hard to believe that's the way the balls came out of the bag, that's for sure."
In contrast, City face newly-promoted pair Cardiff and Hull as well as Stoke in their first five games while Chelsea also meet Hull plus last year's strugglers Aston Villa.
A Premier League spokesman said: "David has put those concerns to us. We have absolutely assured him the process is random and above board. He has accepted those assurances."