We broke the story, TC shoved, pushed and threw punches at bar security on March 15 in Panama City Beach, FL ... and in a video we obtained, you can see him straight-up mauling people.

In fact, we're told Crawford also got physical with AT LEAST two police officers as they tried to break up the scene.

But, Crawford -- who spoke with media for the first time since the incident after Cowboys practice Thursday -- didn't seem sorry for his actions, saying, "I did what I had to do as best I could."

According to the Fort Worth Star-Telegram, Crawford allegedly got into the whole fracas to help his brother at the bar ... and he's hoping when he eventually tells his side of the story to NFL investigators, they'll understand.

"I am going to let God take it," Crawford said. "I can’t speak on it too much. I am going to let God take it and handle everything, however it works out, it works out. Hopefully, they see my side."

Crawford was hit with a misdemeanor charge of affrays for the altercation ... but he reached a deal with prosecutors last month to close out the criminal case ahead of training camp.

We're told in exchange for completing an anger management assessment and keeping his nose clean for the next six months ... he'll have the charge dropped.