Peter Hunt, who worked for the BBC for 30 years including 17 covering the royals until leaving the corporation in 2017, said the Palace should have publicly condemned the abuse.
In November 2016 Harry released a statement in which he condemned coverage of his new partner.
"Meghan Markle has been subject to a wave of abuse and harassment", it said, highlighting, "the racial undertones of comment pieces; and the outright sexism and racism of social media trolls and web article comments".
Hunt said that while Harry had spoken out, there was "silence from the institution". He added: "that was an opportunity where the institution could have made it very clear this was not something they tolerated."
He said part of the issue was the royal household's reluctance to rock the boat with elements of the media, some of whom have been openly critical of the Sussexes.
"Media need royals, royals need media," he said. "[They are] wary of unnecessarily aggravating them. [They] intermittently complain, are privately exasperated [but] very focussed on trying to keep them onside."
The previous coverage of Meghan has come under scrutiny following the revelations this week that the Duchess of Sussex had faced "disgusting and very real" death threats.
On Tuesday, a former head of counter-terrorism at the Met Police revealed a number of threats emanating from the “far right” had been made against the Duchess of Sussex.
“If you’d seen the stuff that was written and you were receiving it, the kind of rhetoric that’s online, if you don’t know what I know, you would feel under threat all of the time,” Neil Basu told Channel 4 News.
Asked if there had been genuine threats to Meghan’s life he replied: “Absolutely. People have been prosecuted for those threats.”
Hunt added: "The broader thing that the institution will always say [is that] they don't start talking about security and you can understand why. This could have started much further back from the get-go. [They could have taken a very clear stance".
The issue of how Meghan has been treated by the royal household was brought firmly into the spotlight this week when it emerged Lady Susan Hussey had made racist remarks to a Black charity boss.
Some have said it validates previous comments by the Duchess of Sussex over claims of racism in the institution and that she badly treated before quitting royal life with Harry in January 2020.
Meghan and Harry have spoken openly before about threats made against them on more than one occasion.
During their interview with Oprah in 2021, the couple commented on their fears at having their security removed by the Royal Family.
Meghan claimed she had written to her in-laws asking for Harry's security to remain in place.
She told Oprah: "I even wrote letters to his family saying, 'please, it's very clear the protection of me and Archie is not a priority. I accept that, that is fine, please keep my husband safe. I see the death threats, I see the racist propaganda, please keep him safe. Please don't pull his security and announce to the world when he and we are most vulnerable'".
Harry added that his family's "justification was a change in [his] status" but that despite this he "got confirmation that [...] the risk" to his life "hasn't changed".
In a 2019 interview about potential threats, Harry said: "[It's] not me being paranoid. If anybody else knew what I knew, be it a father, be it a husband [...] you'd probably be doing exactly what I'm doing as well".
In 2021, a report by Twitter analytics provider Bot Sentinel said Meghan had been the subject of a coordinated hate and misinformation campaign on the platform.
Yahoo News UK has contacted Buckingham Palace for comment.
Watch: Disgusting plots against Meghan Markle investigated
This article was updated on December 2nd.