Similarities between British singer
Petty and Lynne's names were added to the writing credits of "Stay With Me" after the publishers of "I Won't Back Down" noted a resemblance between the songs' chorus melodies.
Petty said there was never any mention of a lawsuit over the song and all is well between the musicians.
"Let me say I have never had any hard feelings toward Sam," Petty said. "All my years of songwriting have shown me these things can happen."
Petty said that most of the time, such similarities are caught before a song gets out of the studio, "but in this case it got by." Smith's song was nominated for this year's Grammys in the song of the year and the record of the year categories.
Although Petty and Lynne are now credited as co-writers of the song, along with Sam Smith, James Napier and William Phillips, if "Stay With Me" wins in either category in which songwriters would be recognized, the two would not receive Grammys.
"Since Lynne and Petty didn't do any new writing for this work, we are considering their original work to have been interpolated by Napier, Phillips and Smith for 'Stay With Me,' " Bill Freimuth, the academy's senior vice president for awards, said in a statement Monday. "Lynne and Petty will not be considered nominees nor will they be considered Grammy recipients should the song win."
Freimuth said the two would receive certificates to honor their participation in the work, as any other writer of samples or interpolated work would.
Smith and Petty came to an agreement on the issue in October, British newspaper the Sun first reported, but news of it didn't emerge until last weekend. In his statement Thursday, Petty said he and Smith don't know how reporters found out about the agreement.
Petty said Smith "did the right thing."