The Girls Aloud singer reportedly told GQ that Lloyd's quip that she is reliant on Auto-Tune was a "slap in the face".
"She's new," Cole said of Lloyd. "She needs to learn a lot.
"I went through hell to get her on that programme. Everyone says stuff at the beginning of their career that they will learn to regret."
She added: "It's disappointing because I fought for her. Maybe I didn't teach her as well as I thought I had."
After Cole warned her Twitter followers to "be careful who you kick on your way up", Lloyd apologised and said that her original comments were a "little joke".
She later admitted that she was "not too surprised" by Cole's reaction, adding: "I think I really did put my foot in it and now I've realised that what I said was wrong, obviously, and I said sorry."
Cole was famously outspoken at the start of her own career as a member of Girls Aloud and had an ongoing feud with fellow popstar Lily Allen, who she dubbed a "chick with a d**k".