Ex-Tennessee football player Jeremy Banks has finally broken his silence after getting kicked off the team last month ... posting a picture with local police officers and apologizing for his "mistake."

Of course, 20-year-old Banks went on an anti-police rant captured on video while being arrested back in September -- saying, "Where I'm from, we shoot at cops."

He also made comments like "Y'all police are some p*****s, bro. Real s**t, I don't f**k with y'all."

Tennesse stuck with Banks after the video came out -- but cut him from the team days later when TMZ Sports learned the linebacker had made violent threats at a female student in August.