Moyes’s first league game as United boss comes at Swansea on Saturday evening.
They then 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 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.”
Nemanja Vidic, meanwhile, trusts Manchester United and Moyes to get it right in their handling of Wayne Rooney.
The striker finally got onto the pitch on Wednesday night, for England against Scotland, for his first appearance of the summer after recovering from a number of injuries, including hamstring and shoulder complaints.
With Hodgson reporting Rooney had suffered no ill effects from his 65-minute work-out, he must now be in contention for at least a place on the bench at Swansea, even if it is probably too much to believe he will start.
Yet Rooney’s state of fitness does not address the clear desire he has to join Chelsea, who have already had two bids turned down for the 27-year-old.
United have continued to insist all summer the former Everton man is not for sale, a position they cannot back-track on without some serious squirming.
Yet Vidic is happy with still Rooney being there. And he has faith in United to deal with the problem in the correct manner.
“I am not worried as much (about his future). Wayne is training well, the club is strong and know what they are doing,” he said. “I have trust in the manager.
“Wayne had a few small injuries in the last few weeks, but he has trained very well.
“He didn’t have as many games but the season is long and I think he will deal with it.”