The 27-year-old actor died from "blunt traumatic asphyxia" in a freak accident at his Los Angeles home last month when his car rolled backward and trapped him against his gate.
Speaking during an appearance on "The Late Show With Stephen Colbert", Quinto said, "Beautiful, beautiful guy. I don't even know how to talk about it. We already knew this was going to be a bittersweet experience as a result of the loss of Leonard (Nimoy, who died in February 20150.
Anton was mourned at a private service by close friends and family and buried in an "undisclosed location" five days after his death at his home in Studio City, California.
On the night he died, Anton was due at rehearsals but when he failed to show up, his worried friends went to his home to check on him and found his lifeless body.
An investigation is also being held into whether Anton's car was a model that should have been recalled because of a gear-shifting problem.
Quinto previously penned a touching message on Instagram, describing Anton as "enormously talented and generous of heart".