The media glare that follows Boca will now be stronger than ever in Santa Fe on Sunday when the Apertura champions visit promoted Union in their second Clausura outing.
Falcioni told reporters on Friday the squad and coaching staff had ironed out their problems and "we're all going to keep working for... the good of Boca."
President Daniel Angelici had to intervene for practice sessions on Thursday and Friday at their "Casa Amarilla" training complex to be carried out as normal.
According to media reports, players had been angry that Falcioni did not make a public apology for a mistake in Venezuela on Tuesday.
Boca played poorly in their opening group match of the Libertadores Cup, a trophy they have won six times, at debutants Zamora and were held 0-0.
Falcioni criticised striker Dario Cvitanich after taking him off in the second half for disobeying tactical orders and later in the dressing room slammed captain Juan Roman Riquelme, a player he has a fraught relationship with, thinking he had been responsible.
Midfielder Walter Erviti, however, said he was the player who asked Cvitanich to switch from the middle to the right and that Riquelme was not involved.
"I want to make clear the coach never presented his resignation, he only commented whether it might be better for everyone if he stepped to one side," said vice-president Juan Carlos Crespi.
