England took an early lead through Harry Kane's wonderfully worked ninth-minute strike but could have been pegged back before Samuel Umtiti's equaliser midway through the first half.
Monaco full-back Djibril Sidibe made it 2-1 at the break, although it appeared to be advantage England when Raphael Varane was sent off for bringing down Dele Alli and Kane beat Tottenham colleague Hugo Lloris from the spot.
But a dazzling France attack, led by Monaco sensation Kylian Mbappe, continued to tear holes in the England defence despite the numerical disadvantage and Borussia Dortmund winger Ousmane Dembele became the third home player to score a maiden international goal when he sealed victory 12 minutes from time.
"I think in course of 90 minutes I saw things we're very good at. With the ball we caused France problems, created chances and scored two," Southgate told Sky Sports News.
"Then we saw things we have to get better at, without the ball and our managing of the ball at 2-2.
"I thought [England's 3-4-3 system] worked really well, up to the point at 2-2, and gave us good options. We moved the ball well and caused them problems with that.
"Whichever system, we had problems with their pace and power. That athletic ability is what makes them hard to play against
"It is definitely something which France, at all age groups, have. They are blistering and they will cause you huge problems on the counter-attack if you're not supremely well organised."
3 - England have conceded three goals in an international for the first time since November 2012 (4-2 loss to Sweden). Porous.— OptaJoe (@OptaJoe) June 13, 2017
Tottenham full-back Kieran Trippier made his international debut, while Burnley goalkeeper Tom Heaton started for the Three Lions for the first time.
Southgate was encouraged by the performances of both men and also singled out Kane and Manchester City winger Raheem Sterling for praise.
"I think both players had some really good moments and it's difficult to assess without watching it back, but I thought there were definitely positive individual performances," he added.
"Sterling caused problems, Kane in the first 50 to 60 minutes led the line really well. A lot of the play with the ball was good.
"At 2-2, after the sending off, they went up a level in terms of what they were able to find and we didn't manage that period of the game well."