Moore, who won the trophy for her role in 'Still Alice', Moore graciously lauded fellow nominess -- Reese Witherspoon (Wild), Jennifer Aniston (Cake), Rosamund Pike (Gone Girl) and Felicity Jones (The Theory of Everything).
The 46-year-old actress later apologised with a tweet.
"I forgot to mention Marion Cotillard in my speech tonight, and I am mortified. She is exquisite in everything + especially 'Two Days, One Night'," Moore said.
Moore is front-runner at this years Oscars for her poignant portrayal of a professor struggling with Alzheimer's.