The youngsters, including player of the tournament Phil Foden and top scorer Rhian Brewster, decided to turn their tops from back to front during their trophy presentation, so their names were displayed instead of the England badge.
Southgate has shown plenty of support for England's youth players, having included Ruben Loftus-Cheek, Joe Gomez and Tammy Abraham in his latest squad to face Germany and Brazil.
Because of this behaviour, the FA will speak to the World Cup-winning youngsters and Southgate had his own message for the teenagers: humility is vital.
"I balance the fact they are young kids in a real moment of ecstasy, so are they going to think logically about what they're doing?" Southgate said. "However, I think what we would hope in the future is that the Three Lions is the more important thing. It's the badge on the front of the shirt rather than the name on the back.
"But I think it is a good thing to talk to the young teams about moving forward, that we're building for England and it's about the team. It's about winning together and experiences together. It's not about building up any one individual.'
When asked whether that demonstrates a mindset of the individual rather than as a team, the England manager said: "I think that's the nature of society today, isn't it?
"It's difficult to know without asking them. I think some of the Under 20s did it as well.
"It is a bit generational perhaps, but I think a good message from national coaches that we have discussed is let's make that point.
"We don't want to beat those kids with a stick because of what they have done because it is a moment to celebrate but I think humility is really important.
"Young players must recognise you're part of something bigger. When you play for England, that is an important message.
"Whether it is your club or your country, the badge you play for is the important thing. If you're going to be a top player, being selfless is key."