The American TV pundit made the hostile comment on March 5, just hours after Mr Adams posted his eight-long thread in defence of the Duchess of Sussex.
The actor, who played Mike Ross in the hit TV series, has called out the Royal Family for failing to standby Meghan in her time of need and claimed the Firm has “outlived its relevance”.
Mr Adams, who attended Meghan and Harry’s wedding in 2018, appeared to mock the Royal Family in the thread.
He said: “She fell in love, moved to a new country, became a household name across the entire globe and began the difficult work of trying to find her place in a family dynamic that can at best be described as complicated and at worst, seemingly archaic and toxic.”
The actor’s criticism of the Firm continued, he added: “It’s OBSCENE that the Royal Family, who’s newest member is currently GROWING INSIDE OF HER, is promoting and amplifying accusations of ‘bullying’ against a woman who herself was basically forced to flee the UK in order protect her family and her own mental health.
“IMO [in my opinion], this newest chapter and it’s timing is just another stunning example of the shamelessness of an institution that has outlived its relevance, is way overdrawn on credibility and apparently bankrupt of decency.”
The rest of the tweets staunchly defend Meghan, as Mr Adams described her as “an enthusiastic, kind, cooperative, giving, joyful and supportive member of our television family”.
Meghan issued a deeply personal statement over the allegations, where she denied the accusations.
Her spokesman said: “The Duchess is saddened by this latest attack on her character, particularly as someone who has been the target of bullying herself and is deeply committed to supporting those who have experienced pain and trauma.
“She is determined to continue her work building compassion around the world and will keep striving to set an example for doing what is right and doing what is good.”
Her spokesman also described the allegation as “a calculated smear campaign based on misleading and harmful misinformation”.
Buckingham Palace said it will investigate claims the Duchess of Sussex bullied royal staff.
They said in a statement: “We are clearly very concerned about allegations in the Times following claims made by former staff of the Duke and Duchess of Sussex.
“Accordingly, our HR team will look into the circumstances outlined in the article.
“Members of staff involved at the time, including those who have left the Household, will be invited to participate to see if lessons can be learned.
“The Royal Household has had a Dignity at Work policy in place for a number of years and does not and will not tolerate bullying or harassment in the workplace.”
The accusations of bullying came just days before Meghan and Harry’s interview with Oprah aired.