Lancaster's side recovered from a strong start by the French to lead, but the hosts snatched the points late on with a 26-24 victory.
"It was a great performance in lots of ways," PA quotes Lancaster as saying. "We're very proud. Once we get over the initial disappointment we'll take a huge amount of positives from the game.
"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. We've learned a lot from this game. We dominated the middle third and to claw our way back from 16-3 was great."
In the day's other game, holders Wales edged out Italy in Cardiff.