The former Brighton & Hove Albion and Sunderland boss criticised the Ligue 1 club's owners for selling striker Gaetan Laborde to rivals Montpellier without his permission.
Poyet vented his anger and threatened to resign following Bordeaux's 2-1 win over FC Marioupou in the Europa League.
"I am not happy. It is one of my worst days at the club," the Uruguayan told reporters.
"What the club have done with Gaetan Laborde is a disgrace. I think we have to stop here. I told the club not to let him leave until we had bought someone else. They have not recruited and they let Laborde go. I arrived at 11.35am. Laborde was not here. He was in Montpellier. Nobody told me anything.
"I need an explanation from the club - from the owner or the president. They are going to explain to me tomorrow [Friday] and we will see if I carry on or not. Am I going to resign? I don't know."
Following Poyet's suspension, reports emerged claiming that Bordeaux's players refused to train in protest against the treatment of their manager.