"I wanted to stay in the job, but I wanted to do what was best for the mission," he told NBC's "Today" show.
McChrystal resigned as U.S. commander in Afghanistan three years ago after Rolling Stone article that quoted him and his staff making disparaging comments about President Obama and members of his administration.
"I felt whatever that the president felt was best for the mission was what I needed to do, so I was happy to go with whatever decision that he made," the general added.
The June 2010 article ended McChrystal's 34-year military career. He was replaced by David Petraeus.
McChrystal declined to say whether the quotes were accurate, saying, "That's past. I accepted responsibility."
He devotes about 1 1/2 pages to the incident in his 400-page biography published Monday. "I don't think we need another book where we are finger-pointing," McChrystal said.
McChrystal also declined to say what the president told him during a meeting in which the general offered his resignation. He described the meeting only as "very professional."