Emmett Till Family to Lil Wayne -- THAT'S NO APOLOGY!!!

Lil Wayne's "apology" to the family of civil rights icon Emmett Till was NOT REALLY AN APOLOGY ... in fact, it fell way short ... a rep for the Till family tells TMZ.

Earlier today, Wayne fired off a letter to the Tills ... to "acknowledge" the hurt he caused the family when he compared Emmett's violent death with the violent way he has sex with women.

Nowhere in the letter did Wayne say he was sorry for what he did.

Now, Airickca Gordon-Taylor -- Executive Director, Mamie Till Mobley Memorial Foundation and Till Family Representative -- tells TMZ the family does not view the letter as a formal apology.

"While it’s commendable that he has vowed to respect the legacy of Emmett Till and his memory to ‘not use or reference Emmett Till or the Till family in his music,' this statement falls short of an apology, as none is mentioned."