Marseille, who had been chasing a title since their 1993 Champions League triumph, ended their long wait by flooring Girondins Bordeaux 3-1 at the Stade de France.
NEWS:Marseille end trophy drought
The southerners, lying three points behind champions Bordeaux in the Ligue 1 race before Sunday's action, see no reason why they should stop there.
"This makes us hungry for more," Marseille president Jean-Claude Dassier told reporters.
"If we had lost (to Bordeaux), people would have said we were doomed but now we want the title. We will not be content with just the League Cup."
"We can't stop there," he said. "The confidence we got from our wins against Lyon and Bordeaux will help us a lot."
Tough times followed Marseille's Champions League win, the club being stripped of their 1993 French title over a bribery scandal and demoted to the second division.
"Let us enjoy this first," he said. "Then we will have a marathon with five matches in two weeks. We will see after those games if we can afford the luxury and the pleasure of fighting for the title."
