"Thank you all for your love and support at this time," he tweeted Wednesday. "I'm trying figuring out how to be the best person I can be. But it's been a process of trial and error.
"I went on Howard Stern yesterday to provide clarity and honesty about what I'm experiencing but while doing that I shared too much ... it's alright for me to be honest about my own feelings but in retrospect some of the information I provided involved others and for that I am sorry and humbled."
Before signing off, he wrote that "life is a process of spiritual evolution. I'm sure Courteney and myself will emerge from this painful time better people for what we've learned."
During his racy chat, Arquette, 39, revealed that he and Cox, 46, stopped being intimate months ago, that he had been intimate with a cocktail waitress and that Cox ordered the separation because she felt like she was his "mother" and not his wife.
Stern, 56, defended Arquette on his show Wednesday. "He was protecting his wife and kid by telling the truth," said Stern.
"He handled himself very well," Stern also said. "He didn't hide away in his house. He went on a legitimate show and spoke his mind, and it was refreshingly honest. Anyone who heard it knew he was being honest."