Thomas, 44, was caught on camera saying, "I drink till I think I'm Australian... And then keep drinking till I'm a black Australian," during his Melbourne show on Friday.
The audience was quick to boo Thomas for the comment, which was taken as a dig at Aboriginal Australians.
"I would like to take an opportunity to further explain the comments I made in Melbourne last night," the former Matchbox 20 frontman wrote on Facebook.
"First, please understand that I did not intend to make a joke about race," he wrote. "I have seen people comment that after coming here for so long I should know that there is a connection between the indigenous peoples of Australia and a stereotype involving drinking. Embarrassingly, I truly didn't."
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Thomas added that his "joke" was only meant at his own expense, and had chosen to use the analogy "at random" to represent things he is not.
"Again, if I had any idea of the stereotype I would have chosen another example," the singer continued. "There was absolutely no malice even in jest. I was so ignorant to the situation that when I heard people groan I actually thought they were being racist."
The musician said that after finding out the connotation of "black Australian" he "sat in my room and I cried."
"I am truly sorry for how this came across, most of all to the indigenous people here. Australia has been so good to me for so long that I'm embarrassed I don't know more about the history and the culture," he wrote.
The "Little Wonders" singer promised to use the opportunity to "rectify" his mistake.
Fans commended Thomas for apologizing, with one follower writing on Facebook, " I am very glad to read you're going to take time to learn about Aboriginal culture while you're here. Thank you for listening, and for being honest, remorseful and open to learning."