Bastia slumped a 2-0 defeat at Ligue 1 champions Paris Saint-Germain on Saturday and footage emerged after the game that appeared to show Brandao, who is in his maiden season with the club, headbutt Motta in the tunnel.
PSG claimed the incident was an "assault" and revealed that Motta had suffered a broken nose.
However, while Bastia have criticised Brandao, they will leave any punishment to the French football authorities.
"SC Bastia unequivocally condemns the gesture of striker Brandao on Thiago Motta after the final whistle of the match between PSG and Bastia," read a statement on the club's official website.
"Pending additional news, Sporting [Bastia] reserves any possibility of further action in this matter."
Bastia went on to suggest that Brandao had been provoked, adding: "We lament the equally unacceptable behaviour or some players who are constantly insulting and provoking their opponents."
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