9:51 AM PT -- A spokesperson for Amber tells TMZ ... "We believe the court made errors that prevented a just and fair verdict consistent with the First Amendment. We are therefore appealing the verdict. While we realize today's filing will ignite the Twitter bonfires, there are steps we need to take to ensure both fairness and justice."
Johnny doesn't seem concerned Amber's followed through on appealing the verdict. His rep tells TMZ ... "The jury listened to the extensive evidence presented during the six-week trial and came to a clear and unanimous verdict that the defendant herself defamed Mr. Depp in multiple instances. We remain confident in our case and that this verdict will stand.”