Films that have won more Oscars than Carol:
-Harry and the Hendersons
-Jerry Maguire
-How the Grinch Stole Christmas
-Pearl Harbor
-Crash
-The Golden Compass
-The Blind Side
-Avatar
-Alice in Wonderland
-The Wolfman
-The King's Speech
-The Iron Lady
-The Big Short
-Spotlight
-Son of Saul
-The Danish Girl
So clearly Carol wasn't eligible.
It was just too good.