Friday (AEST) saw Bordeaux qualify for the UEFA Europa League play-off round after defeating Mariupol 5-2 on aggregate but Poyet was furious post-match after the departure of key player Laborde as he threatened to quit.
Having already lost star Malcom to Barcelona, Laborde was sold to Ligue 1 rival Montpellier without signing a replacement and notifying Poyet, according to the Uruguayan boss.
Poyet, who only arrived in January after leaving Chinese Super League outfit Shanghai Shenhua in September last year, told reporters: "I'm not happy, it's my worst day at this club.
"What the club did today with Gaetan Laborde is a disgrace, I asked the club not to let him leave until we bring in a player. But they didn't recruit and they have allowed Laborde to leave."
"When we arrived at the hotel for today's match, Laborde wasn't there. We called him and he was in Montpellier. Nobody told me," Poyet said.
"I will make a decision. I don't know if this will be the end for me [at Bordeaux]."
Bordeaux, which lost 2-0 to Strasbourg in its Ligue 1 opener, faces Toulouse on Monday (AEST).