Odom tweeted "Seeing the snakes" on Tuesday night in his first post since his Aug. 30 arrest.
He followed with an extended tweet from his verified account that referenced his estranged father.
"Won't continue 2 speak on this but I have got 2 let this out real quick. I have let this man and many others get away with a lot of (expletive). He wasn't there 2 raise me. He was absent ALL of my life due to his own demons. My mother and grandmother raised me. Queens raised me," Odom tweeted.
He went on to credit the family of his wife, Khloe Kardashian, for being "the ONLY ones that have been here consistently 4 me during this dark time. Only person 2 blame is myself. Say what you want about me but leave the ones who have done nothing but protect and love me out of this! This goes out to everyone!"
Odom has been mostly silent on Twitter for nearly three months, although on July 12 he tweeted in part, "Wifey is real," a reference to Kardashian.
Odom, who played for the Los Angeles Clippers last season, is a free agent. He has yet to sign with a team. NBA training camps open next week.