Hill had the opportunity to deny using the word -- Stern said he couldn't really hear it in the clip -- but the "22 Jump Street Star" wouldn't let himself off the hook, saying, "What I said in that moment was disgusting ... I shouldn't have said that."
Hill -- who has been active in supporting gay rights -- took the blame for his remark ... though he did say the pap had been following him around all day and saying hurtful things about his family.
Hill's apology was near perfect -- he did play the "gay friends card" at one point ... telling Stern he just happened to be spending the rest of the day with a gay friend who is getting married soon.
A rep for the Human Rights Campaign, which has worked with Hill in the past, tells TMZ, "All around the world, LGBT young people go to bed at night and stare at the ceiling, sleeplessly wondering what awaits them the next day at school or at church or even in their own home. Hateful words like the one Jonah used are more harmful than he can ever know, especially to kids who hear nothing but negativity about being LGBT. We're glad to see that Jonah is willing to turn this into a teachable moment and we hope others will learn from his mistake."