The 65-year-old singer-songwriter vowed not to talk about the separation, telling Radio Times Magazine he wanted to keep his dignity. But he did say the experience was "a very painful thing."
"As Winston Churchill once said, 'If you're going through hell, keep going!"' McCartney told the magazine. "The only solution is to remain dignified. If I don't keep a silence about it, I lose this idea of being dignified."
McCartney's divorce has become the most sensational marital breakup in Britain since Prince Charles and Princess Diana parted ways more than a decade ago, and the divorce is widely expected to be Britain's most expensive. McCartney and Mills announced in May of last year that they were splitting after four years of marriage.
Journalists thronged Britain's Royal Courts of Justice Thursday when the pair appeared before a judge amid reports that they were close to a multimillion pound settlement.
British media said the hearing was the couple's last chance to privately come to an understanding before having to do that in public in a High Court case next year, but the two left separately without making any comment.
"It's been a difficult time," McCartney told the magazine. "But music is a great healer. Music is the therapy for me. In fact, going through difficulties has only concentrated my desire to make good music."
McCartney also spoke of his admiration for the British monarch, calling Queen Elizabeth II a "babe."
"I've got a lot of time for the queen. She's fun, she's funny, she's amazing," he said. "The queen's a babe!"
"I know what fame is. But she knows what real fame is."
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