Marler, who faces a World Rugby disciplinary hearing on Tuesday for making the remark in England's 25-21 win, said in a statement on Monday he would accept any punishment handed down.
"I'm not a racist. What I said to Samson was out of order and wrong and I am sorry it was said," he was quoted as saying by British media.
"Whatever happens to me I will accept. I'm sorry to anyone who was offended. Saying it was 'in the heat of the moment' isn't an excuse but one comment, one mistake, does not make me a racist."
Rugby's governing body said Marler's remark "amounts to misconduct and/or a breach" of its code of conduct.
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The Harlequins player apologised to Scarlets player Lee, who is from the traveller community, during the halftime break.
England coach Eddie Jones reprimanded Marler while Lee and Warren Gatland played down the comment as banter before the Wales coach later apologised for saying that.
The Welsh Rugby Union said it was disappointed with a Six Nations decision not to punish Marler who could have been handed a four-week suspension.
The 25-year-old played in England's final game of the championship and came off the bench during a 31-21 win in France that clinched the Grand Slam.
(Writing by Ken Ferris; Editing by Tony Jimenez)
