The Argentine had been linked with an exit from the French club for months after a tumultuous first season in charge of Marseille - after remaining in the title race for most of the season, they slumped to a fourth-place finish.
Marseille's woes continued in the first tie of 2015-16, as Andy Delort's goal consigned the club to defeat at the Stade Velodrome, and Bielsa confirmed after the game that he had already chosen to resign due to disagreements over his new contract.
"I thank the fans who have always been behind me during games and every day," he said. "I have finished my work here, I will return to my country. I put everything I have into this team.
Je viens de démissionner de mon poste d'entraîneur de l'@OM_Officiel. #OMSMC pic.twitter.com/2TGeqkSWXk
— Olympique Marseille (@OM_Officiel) August 8, 2015
"I do not regret having done what I did and I refused several proposals to stay at Marseille. I adapted to changes at the club. But, after three months of discussions, I could not accept that there were continual changes in the terms of my contract."
The 60-year-old - who has been linked with the vacant role as Mexico head coach - also touched on the game itself, insisting he did not expect his side to fall to Caen.
"I am sad and frustrated because I did not expect this defeat," he added. "There is no excuse for this. In the first half we had problems, but the second period was satisfactory and we could have won."