Jephson speaks as someone who was at Princess Diana's side for eight years (including when she sued a British tabloid for taking photos of her working out in a gym).
The private secretary noted that the slowness of the trial eventually "deflated" the emotions surrounding the case and effectively cost the Princess of Wales the public's sympathy.
"In the heat of battle and gripped by self-righteous indignation, the royal hand reaches resolutely for the mighty sword of truth and…waits. And waits," Jephson said.
"Unless the head of the offending editor(s) can be served up on a plate with the speed to which royal customers are accustomed, the whole business can start to feel like a bad idea. Somebody else’s bad idea, naturally.
"Eventually, with the Princess of Wales, our legal champions reached a settlement, but by then it was all rather deflating."
What's more, Jephson said that the settlement "didn’t feel like a victory parade and, funnily enough, next day the familiar faces of the press pack wore expressions that were everything except contrite."
Mr Jephson also disagreed with those who drew comparisons between Princess Diana and the Duke and Duchess of Sussex.
"Diana may have been something in the mould-breaker stakes herself, but she never ducked Balmoral, lectured voters on democracy or borrowed invective more normally found in the White House to communicate with a free and fundamentally friendly press," he said.
Last week, Meghan Markle filed a High Court claim against the Daily Mail after it allegedly published one of her private letters to her father, Thomas Markle.
While on their royal tour of South Africa, Prince Harry released a statement on Tuesday evening to the Sussex Official website, explaining that the alleged incident had been an incredibly painful one for them to cope with.
The statement reads: "As a couple, we believe in media freedom and objective, truthful reporting. We regard it as a cornerstone of democracy and in the current state of the world – on every level – we have never needed responsible media more.
"Unfortunately, my wife has become one of the latest victims of a British tabloid press that wages campaigns against individuals with no thought to the consequences – a ruthless campaign that has escalated over the past year, throughout her pregnancy and while raising our newborn son."
WATCH: Meghan Markle gets emotional during heartbreaking speech
Prince Harry then wrote about his fears for the Duchess of Sussex, and that the "bullying" mirrors that which happened to his mother, Princess Diana.
He wrote: "Though this action may not be the safe one, it is the right one. Because my deepest fear is history repeating itself. I’ve seen what happens when someone I love is commoditised to the point that they are no longer treated or seen as a real person. I lost my mother and now I watch my wife falling victim to the same powerful forces."
The claim is being filed against the Mail on Sunday over the alleged misuse of private information, infringement of copyright and breach of the Data Protection Act 2018.
Meghan Markle will be represented by law firm Schillings.
