Mrs Obama made the controversial remark during an appearance on Jimmy Fallon’s The Tonight Show. She also claimed she felt awkward when Mrs Trump presented her with a Tiffany gift box. Mr Morgan wrote in The Daily Mail: “Melania Trump must have winced with anger and humiliation.
“Michelle inexplicably decided to plunge the b**chy knife firmly into the back of her successor as First Lady.
“How sad to see Michelle Obama, a woman I greatly admire, go so low simply to belittle her successor.”
During her appearance on The Tonight Show, Mrs Obama said her reaction to leaving the White House after Donald Trump’s election win was “bye, Felicia”.
Ms Obama was on the show to promote her memoirs, currently the best selling book this year in the US.
Mr Morgan argued: “Michelle Obama likes to pride herself as being street-wise and down with the kids.
“She is a very smart woman so she will have known that ‘Felicia’ is a very similar phonetic name to ‘Melania’, so it would have been obvious to whom she was referring.”
Mr Morgan has enjoyed a friendly relationship with Trump ever since winning Celebrity Apprentice in 2008.
Earlier this month he wrote an open letter to Trump urging the President to employ him as his Chief of Staff.
He commented: “The key thing is to have someone at your side that understands you, likes you and commands your respect.”
However, Mr Morgan’s bid was unsuccessful as Trump selected former Congressman Mick Mulvaney instead.
Mr Morgan has engaged in a number of high profile spats this year, including with singer Ariana Grande and model Tess Holliday.
However, the TV star insisted he remains an admirer of Ms Obama.
He described the former first lady as “a delightful person. Warm, friendly and highly personable”.