Two opening-quarter tries from Yoann Huget helped France into a 16-3 lead, but Mike Brown and Luther Burrell crossed to lead a stirring Red Rose fightback.
But having drawn upon all their reserves of character to edge 24-19 ahead, a brilliant 77th-minute finish from the dancing Gael Fickou and conversion by Maxime Machenaud left England shellshocked.
Lancaster took pride in the fight displayed by his team in a chaotic and compelling opener but recognised that after finishing Six Nations runners-up for two successive years, only victories in the biggest matches are acceptable.
"It was a great performance in lots of ways. We're very proud. Once we get over the initial disappointment we'll take a huge amount of positives from the game," Lancaster said.
"Games are never won or lost in one moment. Everything matters at this level. It was a great Test match played by two great teams.
"Overall the positives of the performance will outweigh the result, but we recognise we need to win big games.
"Five of our pack made their first start in France. They were the youngest pack in the championship and they did extremely well.
"We've learned a lot from this game. We dominated the middle third and to claw our way back from 16-3 was great."
Both of Huget's tries were preceded by cruel bounces following kicks ahead, although England's wounds were also self-inflicted as they had committed mistakes themselves in the build-up.
"Perhaps the bounce of the ball didn't go our way, but we can only control the things we can control," Lancaster said.
"We can't rely on the bounce of the ball, we need to be out of sight by that point."
France, who finished bottom of the table last year, have been installed as Six Nations favourites in the wake of their victory, yet for much of the match England were in the driving seat.
"We were very disappointed to concede the try. Credit to France for creating the try inside their own half," Lancaster said.
France head coach Philippe Saint-Andre celebrated a triumphant start to 2014 and highlighted the impact made by the two-week international training camp his players were granted by their Top 14 clubs.
"We were lucky to score two quick tries and then we had a very high quality first half," Saint-Andre said.
"The second half was more difficult and we missed a few tackles. When we were 16-3 up we mismanaged the game.
"We were less aggressive and they put us under a lot of pressure. But when we had the ball there were more openings because England were winning fewer collisions.
"We must remember we have won the game and this is a very good start for 2014.
"This is not a revolution, more an evolution. Without these two weeks of preparation we wouldn't have won this game, so thank you to the clubs.
"Modern rugby is very demanding so we really needed this preparation time."
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