The incident, which was first reported by the Dallas Morning News, took place at Sherlock's -- a Dallas-area bar -- on Monday. Hamilton's teammate, second baseman Ian Kinsler, was present as well.
"I had a weak moment on Monday night in Dallas," said Hamilton, stating the situation was brought on because of personal reasons with a family member. "I walked to a restaurant to have some dinner and...ended up ordering a drink. I had three or four drinks."
According to Hamilton, Kinsler, who arrived later, was unaware that Hamilton had been drinking. When the restaurant closed, the pair went across the street to another establishment and talked for "25 to 30 minutes" before Kinsler dropped Hamilton off, asking "You're not gonna go back out or anything are you?"
Hamilton said he did go back out and "had some more drinks" at the establishment he and Kinsler had just left.
"No drugs were used at all. I never though about it. I've had two drug tests since Monday so I have no concerns there at all," continued Hamilton, who is drug tested three times a week due to prior substance abuse issues.
This is the second public relapse for Hamilton, who has suffered from alcoholism and drug abuse in the past and had been suspended for over three years early in his career. In 2009, the website Deadspin.com published photos of the then-27-year-old All-Star drinking and taking shots with several women at a bar in Tempe, Arizona.
"There were no pictures taken of me having a beer with somebody or anything like that," he said of Monday's incident.
Hamilton, who did not take questions from the media, failed to speculate on whether the episode would affect his contract situation. The 2010 American League MVP is in the final year of his contract and is eligible for free agency at the end of the season.
"As far as baseball and the Rangers, they've shown nothing but support to me and tell me they will continue to support me," he said, adding "I'm sorry (the press conference) had to be this way. It would've been nice if it was talking about a contract. We'll put that on the back burner for awhile."
The reserved Hamilton also offered his amends, saying "For everybody that I've hurt, for everybody, fans, kids, people who have addictions, I apologize. When you're doing this you don't mean to hurt anybody. You only think you're hurting yourself, but as I know, it hurts a lot of people."