Sarah Michelle Gellar is mourning the death of her "Buffy the Vampire Slayer" costar Anthony Head ... and her tribute is sure to make fans bawl.

Not long after news broke that Head -- who played Rupert Giles -- died of complications from pneumonia ... SMG shared her heartbreak on Instagram.

Along with several snaps from the classic '90s series. Sarah wrote ... "'Tell Giles I figured it out and I’m ok.' Well, I don’t have it figured out, and I’m not ok. But I know I’m the lucky one because I knew you. Thank you to Daisy and Emily, who not only shared their dad with me, but with the world."

Fans know those are among the final words from Buffy in what was supposed to be the series finale in season 5 ... before the show got picked up for two more seasons at another network.

Anthony recently appeared in "Ted Lasso" as former football club owner Rupert Mannion, and also had roles in "The Iron Lady," "Persuasion," "The Inbetweeners" and "Manchild" ... among others.

He was 72.

RIP