On Twitter, Cohen defended the question, agreeing with a fan who believed it was "relevant."
During the show, conversation between the two got a little tense after the host asked the "Unbreakable Kimmy Schmidt" actor about his costar in the upcoming movie "My Name Is Dolemite," Eddie Murphy.
While Burgess avoided any drama on the show when Cohen said Murphy "was very problematic for the gays" earlier in his career, the actor dragged the host over it on Instagram this morning.
"She can be a messy queen! Yes I said it! Don't care he knows either! He should remember his talk show isn't an episode of the real housewives of Atlanta," wrote Tituss on Monday.
"It's a place where artists come to talk about art and have a little fun. NOT a place to rehash old rumors or bring a star negative press," he continued. "Sunday was a display of ratchet behavior by a well connected man having a blatant disregard for one of his guests."
"If only time were taken to know who I am and not assuming that I am the character I play on tv, he would know how to conduct a proper interview with at all," the post went on. "I received 4 Emmy nominations for acting! NOT for being my self. He was lucky I had my wits and Christian values THAT day. Always keep it classy. Being friends with other talented celebrities doesn't make you talented it makes you friends with other famous celebrities! He should rip a page from Anderson Cooper and learn how to do his job."
On Sunday's episode, Cohen first asked Tituss if Murphy was "cool to work with." The actor's response: "He was wonderful to work with. He is a brilliant man and I'm so excited for the younger generation who do not know Eddie Murphy, will learn why he is the legend that he is."
"I just wonder if you got close at all, because he was very problematic for the gays at one point when I was coming up," Cohen then said.
"Oh I see, he wasn't problematic for Tituss and we had a wonderful time," he responded. "We talked about 'Dreamgirls' and he should have won the Oscar I believe. He was great, any troubles he may have had with gay people I guess are gone, because he loved me."
Andy also caught Burgess making a comment to someone off-camera. When called on it, Tituss then told him, "Keep going girl, do your show." Fellow guest Laverne Cox also said Murphy's past comments were made "a long time ago, people can evolve."
Responding to a fan who said the show was "the most awkward #wwhl" they'd ever seen and thought the question was "relevant," Cohen responded saying, "I did too! Awkward is right."
I did too! Awkward is right— Andy Cohen (@Andy) July 29, 2019
Cohen previously spoke out about Murphy using homophobic language during his old standup shows during a conversation with Kevin Hart about his own controversy back in January.
"I have to tell you my own personal thing, relating to being at an Eddie Murphy concert in 85," Cohen recalled. "Every other word out of his mouth was f----t and everyone was laughing, I literally went in the bathroom and started crying." Cohen then said he was "happy" Hart had moved away from using that language himself.
Murphy apologized for his language and AIDS jokes targeted at the gay community from his '80s show "Delirious" in 1996, saying he "deeply" regretted "any pain" his comments caused. "Just like the rest of the world, I am more educated about AIDS in 1996 than I was in 1981," he added at the time, "I think it is unfair to take the words of a misinformed 21-year-old and apply them to an informed 35-year- old man."
"I know how serious an issue AIDS is the world over. I know that AIDS isn't funny," his statement continued. "It's 1996 and I'm a lot smarter about AIDS now."