In his first campaign as Red Devils boss, the Scot faces Chelsea at home before travelling to neighbours City and Liverpool in the opening five games.
|14/1||Manchester United are 14/1 with William Hill to take one point from their first three games
"I find it hard to believe that's the way the balls came out of the bag, that's for sure."
United start at Swansea City on Saturday and the Premier League has moved quickly to reassure Moyes over the selection process.
A competition 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."
Last year's runners-up, Manchester City, face Newcastle first before playing newly promoted Cardiff and Hull City in Manuel Pellegrini's first campaign in English football.