Snelling was arrested early Friday morning and did not make the trip to Tampa, Fla., for Sunday's game against the Buccaneers.
"I just want to start off first apologizing to my family, my teammates and my coaches for the actions that followed me this past weekend," Snelling said. "Also want to apologize to our owner, Arthur Blank, and our general manager, Thomas Dimitroff, and our head coach, coach [Mike] Smith, for my actions. I made a mistake and I'm very apologetic about it. And I'm ready to move forward from it.''
Snelling was charged with misdemeanor marijuana possession (less than 1 ounce) and possession of drug paraphernalia. Winder, Ga., police Officer Chris Cooper said Snelling was arrested following a traffic stop. Cooper said officers pulled over Snelling's SUV after noticing it weaving and crossing the center line. Cooper said officers smelled marijuana inside the vehicle and determined Snelling did not have a valid driver's license or insurance. He also was cited for improper use of a dealer plate.
Snelling was released after posting $3,121 bond.
The seventh-year player emphasized Monday that it was his decision not to make the trip to Tampa and not a form of discipline from the team. He said he took the time to reflect on himself and apologized for not being there with his teammates.
The organization wanted Snelling to be in Tampa. Teammate Steven Jackson even talked about Snelling needing to "be around his brothers" in a time like this.
"Ultimately, I had to make the best decision for myself and for my family," Snelling said. "Under the circumstances, there's nothing more that I wanted to do than be with my team.
"[Jackson] is absolutely right in what he's saying. It wasn't a good feeling not being with my teammates. But all my guys, they rallied around me even though I didn't have the opportunity to address them at the time. I knew that they were with me."
Snelling could remain a key component of the Falcons' running game moving forward, although Antone Smith is expected to get more touches after rushing for 88 yards on two carries -- including a 50-yard touchdown run -- in Sunday's 41-28 loss to the Buccaneers.
Snelling talked about whether he'd be refocused after dealing with the off-the-field issue.
"My attitude on how I approach the game on a week-to-week basis is always the same," Snelling said. "I don't want to make it seem like this situation makes me more motivated."
The NFL is aware of Snelling's situation and is reviewing the matter.