The Colombian singer, 45, split from the FC Barcelona star in June after 11 years of dating.
The duo share two sons, Milan, nine, and seven-year-old Sasha.
“I’ve remained quiet and just tried to process it all. Um, and yeah, it’s hard to talk about it, especially because I’m still going through it, and because I’m in the public eye and because our separation is not like a regular separation,” she told Elle magazine.
“It’s been tough not only for me, but also for my kids. Incredibly difficult.”
Shakira said she had done her best to “conceal the situation” from her children to “protect them”.
But she added: “They hear things in school from their friends or they come across some disagreeable, unpleasant news online, and it just affects them, you know?”
Pique is now reportedly in a new relationship with 23-year-old PR student Clara Chia Marti.
During the interview, Shakira also spoke about how the breakup was compounded by her dad suffering a fall and being rushed to hospital back in June.
“Sometimes I just feel like this is all a bad dream and that I’m going to wake up at some point. But no, it’s real.”
She went on: “What’s also real is the disappointment to see something as sacred and as special as I thought was the relationship I had with my kids’ father and see that turned into something vulgarized and cheapened by the media. And all of this while my dad has been in the ICU and I’ve been fighting on different fronts.
“ Like I said, this is probably the darkest hour of my life. But then I think about all those women around the world who are going through hardship, who are going through a situation as bad as mine or as difficult as mine or worse.”