Duffy, who is currently on loan at the Parkhead side from English Premier League outfit Brighton, posted the messages on his account with the comment: “There's abuse which is fine but surely there's a limit.”
The Facebook-owned app initially promised to investigate the incident following initial reports, but Sky Sports reports that the firm has decided that the abuse, which included sectarian slurs and mocking references to the death of the player’s father, was an isolated incident and that the user responsible has deleted the messages and apologised for their conduct.
Duffy had earlier closed both his Twitter and Instagram accounts in the wake of personal abuse but reopened his account on the photo-sharing platform just days before receiving the sectarian abuse.Instagram has since pledged to work harder to stamp out online abuse, and has vowed to introduce stricter repercussions for those guilty of abuse – including the removal of accounts.
A number of players have been subjected to racial and sectarian abuse on social media.
Duffy's Republic of Ireland international team-mate James McClean had threats sent to him via Instagram while Aberdeen forward Florian Kamberi was also targeted.
Instagram has reportedly restricted the account of the person behind the comments sent to former Hibs and Rangers striker Kamberi, which read: “I can’t wait for the day you die.”
The user faces permanent deletion of their account if they breach Instagram’s stringent guidelines again.