The rapper told The Mirror that he was "young" when the incident occurred in January 2010, but added that the caller should not have spoken to him the way she did.
Dappy had appeared on The Chris Moyles Show with N-Dubz bandmates Tulisa Contostavlos and Fazer, when caller Chloe Moody called into the station and criticised the group and Dappy in particular.
The following day, Moody received a number of threatening text messages from the star, after he had made a note of her mobile phone number.
Dappy said of the incident: "I was only young at that time, but she shouldn't have been so rude towards me. Dappy won't do that again. I was a bit naughty at that time."
The 25-year-old also confirmed he and X Factor judge Contostavlos had reconnected after having fallen out over a rap he performed about Simon Cowell.
"Two days ago, we cried in each other's arms. It was beautiful - I'd got my cousin back," he said.
Watch Dappy's music video for 'No Regrets' below: