In a preview for the episode, Singer questioned, "How smart can Dennis be? I mean, he was on drugs." The episode was film three weeks after Shields' death, Peoplereports.
"I cringed when I saw what I said about Dennis in tonight's episode," Singer, 62, wrote. "It definitely wasn't one of my finer moments. I respected and liked him very much and I sincerely apologize to his family and Bethenny for my thoughtless comments."
Also on Wednesday's episode, Frankel opened up to Dorinda Medley about Shields' proposal prior to his death on Aug. 10, the cause of which was ruled "undetermined" after an autopsy was not performed due to religious objection. Authorities initially suspected it was an accidental overdose.
"It was not even close to a perfect relationship. Part of me died inside, it was really bad, but I couldn't get out, though, either," Frankel, 48, said. "I loved him so much and we were family and my daughter was so close to him and I knew him for so many years."
"He proposed on April 25th... I didn't tell anybody that... It's very sad," she continued of the 51-year-old. "... So I kept it to myself because I didn't want another circus of my life. I didn't want to start telling people. We had our own private engagement."
"He bought Bryn a ring too," she added of her 8-year-old daughter with her ex-husband, Jason Hoppy.
A source previously told ET about Shields' April proposal, saying, "She wanted to marry him, but there were some things that needed to be worked out first and some hurdles to overcome. He was her family, her best friend, her partner."