The post-match flashpoint came as Manchester City's announcer named every member of the winning squad and backroom staff individually as they collected their medals — a practice Manchester United coach Fletcher said he had never witnessed at a cup final in his career.
City officials noted that Fletcher had approached FA representatives at the time to register his objection while the presentations were still taking place.
"Not only to watch a team lift a trophy, but to be a Man City parade when it's an FA Youth Cup final. I've never heard individual coaches be shouted out, every individual player be shouted out. That doesn't happen in cup finals."
He extended his frustration to the FA for what he described as a series of failures surrounding the game, beginning with the venue.
"I'm disappointed in the FA for everything that's gone around this game, for the location, for everything. And then our players having to deal with that."
The choice of the Joie Stadium — which holds around 6,000 supporters — rather than the Etihad Stadium was contentious throughout the build-up. City cited construction work around the Etihad as the reason the final could not be played there. Manchester United offered Old Trafford as an alternative venue; City declined.
"It's an FA competition. It should never have been like that. But that's my one gripe for tonight. The best team won. Compliments to them."
He urged the governing bodies to reflect on a set of circumstances he described as damaging to historic youth competitions.
"If you see the things that have gone on throughout this game, it's a historic competition. There's been a lot of disappointments in the build-up. Hopefully people take a step back now when they've come away from it. There's a lot of learning to be done for the Premier League and for the FA for these historic competitions."
He also noted that some United players would be required for an Under-21 fixture within 48 hours of the final, adding to what he called a "lot of difficult dynamics."
Despite his frustrations, Fletcher reserved praise for City's head coach Oliver Reiss and the winning side.
"Man City have got a fantastic manager. He's a great, really nice guy. Dead respectful. Coaches his team the right way. No antics on the sidelines between both of us. I've got massive respect for them and their players."
The winning goal was scored by Reigan Heskey, son of former England and Liverpool striker Emile Heskey.