The originator of today's phrase was probably Boston Globe columnist Ellen Goodman, who has been running an annual "Media Culpa" column since 1988 (in prior years, she used the phrase "mea culpa," instead):

"And now once more, in the interests of a clean slate, a fresh start and a genuinely new year, it is time for my annual Media Culpas. This has become a rite of passage for me, a cleansing confession of the errors of my way through the past year." —Ellen Goodman, "It's media-culpa time again," The Boston Globe, December 29, 1988

Media culpa is a play on the Latin phrase mea culpa, "a formal apology or acknowledgment of wrongdoing or guilt"; literally "(through) my fault."