The 28-year-old smirked and claimed that it was "funny to hear a female" talk about American Football when questioned by Jourdan Rodrigue, a reporter for the Charlotte Observer.
In a video posted on his Twitter account on Thursday, Newton said: "My word choice was extremely degrading and disrespectful to women.
"If you are a person who took offence then I sincerely apologise to you.
"During this process I lost sponsors and countless fans. I realise the joke is on me. Don't be like me. Be better than me."
The Panthers will take on the Detroit Lions on Sunday.