The former Athletic Bilbao boss joined the Ligue 1 club during the close-season and has overseen two wins, a draw and a loss in his four top-flight fixtures so far.
However, Bielsa's future at the Stade Velodrome could be in doubt after his public attack on Labrune's transfer policy on Friday.
"The time for us to build the team is over. The outcome is negative," said the Argentinian.
"I can't see the correlation between the project we agreed upon and what has actually materialised.
"I think, when the president contacted me, he came with some promises that he knew he wouldn't be able to keep.
"I feel it is now necessary to tell the truth about what we envisaged and what has truly happened.
"I would have liked to be told the truth. That's it. If I would have been told the truth right from the start, I might have accepted it. But now that we have already started, I can say it provokes anger in me.
"I repeat, the Olympique de Marseille president came with some promises that he knew he wouldn't be able to keep.
"We planned to build a project with the president, and he knew right from the start that he wouldn't be able to carry it out."
