Marseille, lacking the financial clout to compete with well-funded bitter rivals Paris Saint-Germain and also Monaco, showed some spirit in the second half with Andre-Pierre Gignac bringing them back to 4-3 with a wonderful overhead kick, his second goal of the game.
However, former Marseille player Fabrice Abriel restored the two-goal advantage and although veteran Souleymane Diawara -- who had scored an own goal in the first-half -- made it 5-4 the fans had run out of hope and already headed for the exits.
Marseille's elimination from the Cup follows a week after they were knocked out of the Coupe de la Ligue and carries on a dreadful run which has also seen them knocked out of the UEFA Champions League group stage with no points and in Ligue 1 they trail 18 points behind leaders PSG.
Earlier, three Ligue 1 clubs had been eliminated by sides from lower divisions including Corsican duo Ajaccio and Bastia.
Ajaccio, bottom of Ligue 1, went down 2-1 at home to Ligue 2 side Caen while Bastia also lost 2-1 away at another second tier team, former French champions Lens -- Bastia's city rivals Ligue 2 CA Bastia saved Corsican honour by defeating Niort 5-4 on penalties after the all second tier clash ended 2-2 after extra time.
Lens, presently third in Ligue 2, went through thanks to a beauty of a winner by Senegal international Deme N'Diaye which had coach Antoine Kombouare running up and down the touchline in an exuberant celebration.
Kombouare, formerly coach of Ligue 1 giants Paris Saint-Germain, had made some changes to personnel for the match after being dissatisfied with their performances of late, and he was delighted with the reaction.
"This is one of our best performances of the season," Kombouare said.
"In terms of emotion, this is huge. We didn't back off from the first minute to the last and we have emerged with enormous credit from this game.
"I played my win at all costs card with the players this evening and they didn't let me down.
"I am very proud of them."
Second-from-bottom Sochaux also fell by the wayside as they went down 1-0 away at Ligue 2 side Angers with the experienced Djibril Konate scoring the winner -- what made defeat sourer was that the scorer is a player the losing coach Herve Renard knew well from his time in Africa.
However, Renard, who famously coached Zambia to an emotion-charged win in the 2012 African Cup of Nations, was phlegmatic about exiting the Cup, his boundless and trademark optimism focussing on the positives and the challenge of preserving their Ligue 1 status.
"It may be a paradox but qualifying for the next round wasn't essential even if we would obviously have liked to have gone through," he said.
"Now we have to turn the page and focus on the league where the situation is very difficult (they are ten points from safety). It is important to stay positive."