Frazier accused Lowe of making the suggestion during their time in the fantasy suite when she appeared on the Women Tell All special on Monday (March 3).
Writing in his blog for People, Lowe admitted that Frazier's claim was an "accusation that [he] did not see coming".
"Let me set the record straight - I never said that," he said. "I would never say that. It just doesn't make sense. Of course I had feelings for the other two women. That's been apparent for weeks!
"And not only did I have feelings for them, I was falling in love with them. I even had feelings for women like Des and Lesley, who weren't even there anymore. In that moment on WTA, I felt like it was an attack on my character, so I began to get defensive. I was so stunned by the accusation that I was speechless."
Lowe added that he has no idea what he said to make Frazier believe that he wasn't interested in Giudici or Yenter, but said: "I am sorry if I said anything at all that misled her because that was truly not my intention. I am also sorry that she's still harboring these feelings of resentment. I wish nothing but the best for AshLee, and I hope she finds a great love one day."
However, Frazier insisted that she hadn't made up the claim, telling People: "It is what he said among some other things. I was like, 'Hello? Are you kidding me? That's what you said to me on the overnight date'.
"That's why I was so blindsided. I thought I was going to be the last girl standing, and I wish he'd have extended the same courtesy to me that he did for Sarah and not made me go through a rose ceremony once he decided to send me home. But it is what it is. I have no ill will for him, I'm over him and I hope he finds happiness."
The Bachelor finale - in which Lowe will choose between Giudici and Yenter - will air on Monday (March 11) on ABC.