Sarah Palin's 16-year-old daughter Willow Palin used multiple homophobic slurs -- including the word f**got -- to attack a Facebook user who criticized her mom's new reality show .... TMZ has learned.

During the premiere of "Sarah Palin's Alaska" Sunday night -- a boy named Tre who went to school with the Palin kids wrote a status update that read, "Sarah Palin's Alaska, is failing so hard right now."

The comment sparked an intense response from Willow -- who replied on the boy's wall, "Haha your so gay. I have no idea who you are, But what I've seen pictures of, your disgusting ... My sister had a kid and is still hot."

Willow followed up that comment with another that read, "Tre stfu. Your such a f**got."

Bristol Palin also got in on the smacktalk -- writing a message to Tre saying, "You're running your mouth just to talk sh*t."

Eventually, a message board war erupted -- and Bristol took aim at another person named Jon -- saying, "You'll be as successful as my baby daddy, And actually I do work my ass off. I've been a single mom for the last two years."

After more users began to gang up on the Palins, Willow dropped another message that read, "Sorry that you guys are all jealous of my families success and you guys aren't goin to go anywhere with your lives."