Davis struck Missouri offensive lineman Kevin Pendleton three times with his fists as the two were on the ground, then appeared to knee him in the back after he stood up.
Davis was flagged for unsportsmanlike penalty but was not ejected.
"I would like to apologize to Kevin Pendleton, the Missouri Tigers, their fans, Alabama Fans, and my teammates and coaches for my actions during tonight's game," Davis tweeted. "I allowed my emotions to get the best of me and that's unacceptable. Again I'm sorry and it will never happen again."