The X Factor winner dumped the Tottenham Hotspur striker following reports that he had cheated on her with a 23-year-old model.
Speaking a few days after the split was announced, Burke told The Mirror: "I'm quite naive. I think that comes from me wearing my heart on my sleeve.
"I'm such a loyal person. That's what I give out and I expect to get it back. Sometimes you don't and it does hurt. But that's just the way I am.
"I don't know how to cope with it sometimes, if I'm completely honest. All I can do is get on with it day by day."
Defoe's previous girlfriend Chantelle Houghton recently called him a "cheat" and a "nasty little rat".
The singer's split from Simon Cowell's record label Syco caused the release of her second album Heartbreak On Hold to be delayed.
Following the completion of the LP, Burke explained: "It was challenging making it because I don't like being open."
She said that she had to reveal more to her fans through her music because she felt the need to apologise for the album's delayed release.
The singer also admitted that she'd "love to be settled", claiming she is the sort of person who believes in fairy tales and hopes to marry and have children one day.
Burke's new single 'Let It Go' is out on Monday (May 28). Heartbreak On Hold is released on June 4.
Watch the video for Alexandra Burke's 'Let It Go' below: