Odom was arrested for allegedly driving under the influence of drugs and alcohol last week, shortly after returning home following a brief separation from Kardashian, his wife of nearly four years.
"As much as I wish I were made of steel...I'm not," Kardashian tweeted during the weekend. "I'm pretty damn close to it though hehe."
She previously posted a message on Twitter saying "smile and no one will notice."
Other than the vague online postings, Kardashian has not publicly spoken about her recent woes, which reportedly stem from Odom's alleged substance-abuse issues.
UsMagazine.com said the couple have not been photographed since arriving home in separate cars Friday following Odom's arrest.