The couple welcomed a daughter on Friday (4 June) and have named her Lilibet "Lili" Diana Mountbatten-Windsor, in a nod to both the Queen’s nickname and Harry’s late mother Princess Diana.
However, some people have questioned whether it was right to use the Queen’s nickname and whether the monarch was asked about it.
Goddard has now waded in, saying on Good Morning Britain that Harry and Meghan are being bullied and “can’t do anything right”.
“I don’t believe for a minute that they didn’t talk to the Queen. It’s well known Harry and the Queen have a very close relationship,” said the TV star.
Goddard - who has previously been open about her own experiences of bullying – went on: “It’s about pain. It is about pain and it’s, excuse my French, bloody relentless.
“It’s bullying now.”
“They can't do anything right anyway,” she added.
The presenter said some people have suggested the royal pair should just keep quiet, but insisted it would not change anything.
“This is about pain and it is also about continuous relentless bullying,” she said.
A Palace source recently told the BBC that the Duke and Duchess of Sussex did not ask the Queen about naming their daughter Lilibet.
However, a spokesperson for the couple insisted that the Queen was the first person that Harry had called and said that they would not have used the name if the monarch hadn’t been supportive.