Action Against Discrimination (AAD) called it “both deplorable and unacceptable” for neither organisation to come out against a tweet in which a supporter called the Israeli international a “Jew b******” among other anti-Semitic slurs following Celtic’s 1-0 defeat at Ibrox.
AAD chairman Jonathan Metliss said in a statement: "We are surprised that both Celtic FC and the Scottish Football Association have failed to condemn this behaviour.
"Words cannot describe the abuse directed at both the player and his family in the aftermath of Saturday's match, and for neither of them to come out and condemn the tweets in the strongest possible terms is both deplorable and unacceptable.
"By way of contrast, we wholly support Bournemouth's action to immediately and properly condemn the racial abuse directed towards their midfielder Junior Stanislas at Stoke City at the weekend and we want to see Celtic and the SFA follow suit.”
Bitton was sent off in the 62nd minute of the Scottish Premiership encounter. Celtic, who had been on top for most of the game, would go on to lose the match 1-0 thanks to an own goal from Callum McGregor.
ADD also called on Police Scotland and football authorities to enforce the strongest possible punishment against supporters who sent a racist letter to Kilmarnock boss Alex Dyer and warned about the rise of racism online during the pandemic as supporters are not allowed into stadiums.
Metliss continued: "We also condemn a letter which was sent to Kilmarnock manager Alex Dyer containing racial abuse, and hope that Police Scotland the relevant football authorities, having identified those involved, take the strongest possible action against them.
"In absence of spectators at football matches, the internet has clearly become the forum for all forms of racism and discrimination in football and, as we have maintained on previous occasions, ask Twitter and all social media channels to be more accountable for the messages that appear on their respected platforms."