Speaking on The Graham Norton Radio Show with Waitrose, the author - who was married to the Queen's son Prince Andrew - confessed she "screamed at her TV" when her daughters made their way to St Paul's Cathedral for the Thanksgiving Service on June 3.
WATCH: Princess Beatrice pays touching compliment to the Queen
"Everyone else looked a bit... very serious and they were smiling and really thanking their grandmother for these 70 years," she explained, adding: "I was watching the telly like, 'Well done girls, you're smiling.' I can't get over how beautiful my girls look. When they went off to the Jubilee Thanksgiving Service, wasn't that just beautiful?
"I couldn't get over it. There was Beatrice in blue and Eugenie in orange and they are smiling, right. So grateful... I was screaming at the TV."
Of their upbringing within the royal family, Sarah stated: "I think the way Beatrice and Eugenie are behaving and have behaved, it's just extraordinary."
The royal sisters at St Paul's Cathedral for the Queen's Thanksgiving Service
The mum-of-two went on to speak about her and ex-husband Prince Andrew's different approaches to parenting. "As parents, Andrew very, very much sticks to the Navy schedules and has real discipline. He has always been like that," she said.
"And then along comes the river - that's how I call myself - giving that sense of humour and that sense of joy and sense of little more freedom and I've always been like that with the girls, so they have the best of both."
Mum Sarah with daughters Beatrice and Eugenie
When asked about life as a grandmother, the writer replied: "I think that it's so fabulous to be a granny. And for all those grannies out there. I'm going to own 'super grannie'.
"When I go to see August, he’s 16 months old, he really finds me funny. So for once, I know that he really is thinking I'm funny, and then Sienna, she's just unbelievable. She's only seven months, I'm very very, very lucky."
Make sure you never miss a ROYAL story! Sign up to our newsletter to get all of our celebrity and royal news delivered directly to your inbox.