The 56-year-old came up with the harsh nickname amid rumors that he might return to Good Morning Britain, despite exiting the show in March after the Suits alum, 39, made a formal complaint against him.
The response to Morgan's tweet was mixed.
"Princess Pinocchio how disgusting calling someone that , wonder how you will feel if someone calls your daughter names like that in future years," one user wrote.
However, others made it clear they want to see him on their television screens again.
"Get back on.piers miss you," one fan responded.
"Week day mornings are not the same without Piers," another commented.
"Did anyone take my dressing room?" Morgan added in response to a Daily Express article about his rumored return to GMB.
At the time, Beresford said that he was aware Morgan didn't like Markle because he has made it "so clear, a number of times on this program," adding that the mom-of-two allegedly cut Morgan off in the past, which "she's entitled to do."
During the couple's sit-down with Winfrey, Markle said she previously had "very clear and very scary" suicidal thoughts while she and her husband, 36, were working royals. The former actress claimed that she "went to the institution, and I said I needed to go somewhere to get help," but was allegedly told she could not get help because "it wouldn’t be good for the institution."
"Who did you go to? What did they say to you? I'm sorry, I don't believe a word she said, Meghan Markle. I wouldn't believe it if she read me a weather report," Morgan hit back at the time. "The fact that she's fired up this onslaught against our Royal Family I think is contemptible."
"On Monday, I said I didn’t believe Meghan Markle in her Oprah interview. I’ve had time to reflect on this opinion, and I still don’t. If you did, OK. Freedom of speech is a hill I’m happy to die on," he reiterated on Twitter later. "Thanks for all the love, and hate. I’m off to spend more time with my opinions."
According to the Daily Mail, Markle was not upset by Morgan's comments at the time — but launched the complaint out of concern for how his comments could affect viewers struggling with their own mental health.