Alec Baldwin is finally admitting (and even apologizing) for spewing a homophobic slur at a photog in NYC yesterday ... but shockingly, the slur he's copping to is NOT the F-bomb.

Late last night, Baldwin went to Twitter and wrote, "Rich Ferraro from @glaad informs me that c'sucker is an anti-gay epithet. In which case I apologize and will retire it from my vocabulary."

Of course, Baldwin's referring to the incident outside of his Manhattan apartment ... when he called a photog a "c**ksucking f*g."

Funny, Alec is ADAMANT the F-word he used was "fathead" and NOT "f*g" ... even though you can hear it clear as day in the footage, which we posted on TMZ.

A rep for GLAAD has also issued a statement ... saying, "Mr. Baldwin can’t lend his support for equality on paper, while degrading gay people in practice. It's clearly time he listens to the calls from so many LGBT people and allies to end this pattern of anti-gay slurs."

7:55 AM PT -- Anderson Cooper has also weighed in ... tweeting, "Wow, Alec Baldwin shows his true colors yet again. How is he going to lie and excuse his anti-gay slurs this time?"