The home side, one of the favourites for Euro 2024, impressed in spells but lacked a cutting edge against their disciplined opponents at Wembley and had some shaky moments in defence.
The game appeared to be heading towards a goalless stalemate before 17-year-old substitute Endrick scored in the 80th minute after coming off the bench.
Defeat is a blow for England manager Southgate, who has just the one more match, against Belgium on Tuesday, before he names his squad for Euro 2024 in Germany.
"There were lots of very good performances," Southgate told Channel 4. "It is a top-level game and we have controlled long parts of it.
"We had as many attempts as them on goal but in the end it is that ruthless moment that decides the game.
"We've had a lot of players go on, a couple of debuts and some really important individual performances for us."
England were without several key players including captain Harry Kane and Arsenal's Bukayo Saka through injury.
But Newcastle forward Anthony Gordon impressed on his debut while Aston Villa defender Ezri Konsa and Manchester United's teenage midfield prodigy Kobbie Mainoo won their first caps as substitutes.
"Tonight was the best day of my life," Gordon told the BBC.
"I envisioned it a bit different with a win and a goal. I thought we were the better team but we lacked that cutting edge that they had at the end.
"This is my long-term dream I have had. To achieve it means everything to me."
He added: "We have to find a way of killing teams and putting them to the sword when we get the chance."
