Phelan has penned a three-year deal to remain as assistant manager.
Fletcher told manutd.com: "There are only so many clubs in the world who have a special DNA-type thing. There are less than a handful, and Manchester United is one of them. Mick knows that more than anybody, as you say, having been a massive part of Manchester United's success with Alex Ferguson, and it's important that the players are educated on that by people who know it, and can let them know what it means to be a Manchester United player.
“The standards are different to any other club in the world; the expectancy is different to any other club in the world. And the players have to be educated on that, to not be afraid of it but to embrace it. People talk about the history of the club – we were always told to 'embrace that, feel a part of it, don't be intimidated by it, strive to be like these famous great players'.
“It was an education, and I loved every minute of it. That's what Mick's talking about. The foundations have to be put in place to get us back to that level, and to get the players to realise how special it is to play for Manchester United, [to] want to be here. Learn about the history of the club, so that they're a part of that history one day, of achieving fantastic things."