Brady has been taking some serious heat for the past week ... over a joke in which he says Sarah Palin hates Jeff Ross because he reminds her of "what Trig is going to look like when he's 40."
Wayne issued a statement on Facebook in which he says he didn't write the Jeff joke but explains, "At the end of the day I take full responsibility for saying it."
He adds, "I could defend it as a performer, but I would rather apologize from the bottom of my heart as a father."
"To the Palins, please know that no malice or harm was meant. To the other families who were touched negatively, I hope you'll be able to accept this apology as well."
Brady was at LAX this weekend ... and told us, "It's a roast, but there are people with sensitivities ... and some people were bothered."