England's strategy was the same as for years and years now - play to not lose, don't play to win.
This means running at your opponent with the ball until he fouls you, then you can try to score form the free kick or penalty. Preferably you get a penalty, because its harder to miss a penalty than an open field shot. Plus, if the penalty is saved or hits the post, there's no play on, the defending side can't sweep up the rebound and return it for a quick strike.
So if you get one goal, that's enough. Which is why so many England matches over the years have gone to penalties, because they are usually low-scoring (and boring). The shame isn't that we have lost so many penalty shoot-outs, it is that we have been in so many penalty shoot-outs in the first place. This is also why we have often lost to weaker teams.
England was the same team with the same ideas, just different faces at each position. Same game, same result.
Look at how France won.... the decisive last 2 goals were power shots from outside the penalty box! Outside of a free kick (as you astutely pointed out) or penalty, I've never seen England score goals like that. Why? Maybe it's a lack of talent (although those two near misses were epic fails, especially the set up by sterling and then the other bloke blows it wide of the goal) but I don't think it's all that, it's because that's just not how they are trained... If I was Southgate, I would get every academy in the country to start training kids on how to shoot. Cancel all the training on cross and headers and replace with the basics: kids, you've got to learn how to shoot the ball with power from a distance. I'm convinced this is a style issue.