Dembele was enjoying a growing influence on the game, though, and he was instrumental when France took the lead with only two minutes of the second half remaining.
England went on to win the match 3-2.
And he confessed: "I am afraid there's no magic wand". "I don't think that does any harm".
The former global defender added: "To be honest it has been absolutely what I thought". They are fully committed, I can't question what they've given. But we are recognising where we are short, we are recognising where we can exploit teams. You find out where you are against the very best'.
"We just didn't manage that period of the game as well as we needed to, I thought we exhausted", said Southgate.
The teams then gathered at the centre of the pitch for a minute's silence for those murdered in the London and Manchester attacks.
France's Ousmane Dembele, left, celebrates after scoring his side's 3rd goal while France's Kylian Mbappe looks on during their friendly soccer match between France and England at the Stade de France in Saint Denis, north of Paris, France, Tuesday, June 13, 2017.
Such comments were borne out of the frustration that is only understandable as Southgate looks to turn promise into success. I am afraid there is no magic wand but we are recognising where we are short, we are recognising where we can exploit teams. We're all buying into what Gareth's doing'. "I mean we've given some poor passes away, and that cost us a goal at the end of the game today, but we are keeping the ball better, we are creating chances and looking a threat with the ball".
Although qualification for the 2018 World Cup is nearly given, the recent defeats have thrown some questions top ponder for Southgate which need to be resolved before England head to Russian Federation for global football's showpiece event next year.
The Three Lions boss has suffered a bad spell since replacing Sam Allardyce last September - winning just three of his eight games.
"J'ai clairement vu quelqu'un sauter" — Incendie à Londres
La police a procédé à l'évacuation d'une partie des immeubles et maisons voisins menacés par la chute de débris lourds. Des analyses sont par ailleurs menées vis-à-vis de la structure du bâtiment, grandement fragilisée par les flammes.
"Well, then it's a big challenge then, isn't it?"
"I think both players had some really good moments and it's hard to assess without watching it back, but I thought there were definitely positive individual performances", he added.
On a frustrating night: "We should have got a result".
"Those periods you have really got to control possession and stay calm, and I thought we looked more anxious while they went to 10 and they stepped up a level".
England have won only one of their past seven games against France, losing five.
England were second best against a young, confident French side.
Heaton collected his third cap, but started from the off for the first time at the Stade de France.
"We've got players with bags of quality, it's just putting it together and getting it right". We have a slightly longer vision, the coaching team is settled. It was the same here and that needs to change going into tournaments because we need to beat these teams.
Paul Pogba (France) His touch, presence and brain were far too much for England, and allowed him to dominate midfield.
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