The Ligue 2 side had been on an extraordinary cup run, which saw them reach the penultimate round of the tournament only to fall foul of a spot in the final thanks to goals from Alexandre Lacazette and Bafetimbi Gomis.
"I'm proud of my players. They produced the kind of play I expected of them and gave a positive image of the club and the city," Furlan told reporters after the match.
"At 2-0 down, a lot of teams' heads would have dropped. We had the mental strength to come back into it and make our opponents worried.
"I don't have any regrets. In this kind of game, you only get one or two chances. You can't afford to miss them."
The final will now be contested by Lyon and Paris Saint-Germain.