The former United captain stepped up from his U18 role to take charge as a caretaker after Ruben Amorim's dismissal.
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Fletcher said, "It was an amazing experience. I'm disappointed we didn't win the game, so I can't hide that, but in terms of the experience of leading the team out, preparing the team, the fans, the support, everything like that, it's a pleasure.
"It was an honour, but I can't help but stand here and think that we didn't win the game, so that's my overriding disappointment."
He also said: "I've spoke to the board and I'll be in charge for the Brighton game and then we'll take it from there again. It's one game at a time, so, yeah, recover from this game and then we prepare for Brighton and the FA Cup on Sunday."