The 22-year-old scored a late penalty to earn a point for the Londoners before missing a late chance in the match at Carrow Road.
Osayi-Samuel displayed some of the graphic abuse on his Instagram account with the caption: "It is disgusting and painful to be receiving messages like this".
It prompted a strong statement from the club.
Lee Hoos, QPR chief executive, said: "We completely deplore the abhorrent abuse Bright has been subjected to.
"It astounds me that people feel they can freely post such comments without any fear of reprisal.
"We are working with Instagram and asking them to assist us in identifying the individual concerned. I do feel social media platforms have a duty of care to its users who are victimised in this way."
QPR director of football Les Ferdinand added: "This type of abuse on social media is too commonplace and has to stop. In a society that now rightly places greater importance on mental wellbeing than ever before, how can people be able to set up anonymous social media accounts?
"This will continue and continue until we stop it from being possible. I believe governing bodies across sport - not just football - need to come together to create a powerful voice which calls for social media platforms to change their stance."
Osayi-Samuel is out of contract at the end of the season and has been talked up as a potential target for the Old Firm.