The Merseyside club called the chants “offensive and inappropriate” as Gilmour, who is on loan at the newly promoted side from Chelsea, was targeted during the 3-0 win.
The chants were called out on Twitter by ‘Kop Outs’, Liverpool’s LGBT+ Fans Group, with the Merseyside club adding: “The chant is offensive and inappropriate a message we have repeatedly communicated alongside Kop Outs.
“We urge supporters to remember the inclusive values of the club and to refrain from using it in the future.”
Gilmour has been sent out on loan in order to gain more regular first team football, having been unable to force his way into Thomas Tuchel’s side despite impressing when given opportunities last season.
Diogo Jota, Roberto Firmino and Mohamed Salah scored for Liverpool on Saturday as they got their 2021-22 league campaign off to a flying start.