The 39-year-old stepped down from the BBC Two companion show in May after falling pregnant with her third child Arthur, who was born in July.
Former Strictly Come Dancing contestant Zoe Ball was named as her replacement in early July.
"It broke my heart but Zoe is absolutely brilliant," she told the Daily Mail. "I couldn't do it because I knew Arthur was going to be too little, but I couldn't leave Strictly completely so I do the results show."
Winkleman elaborated that she could never completely quit Strictly, as it has become a huge part of her family life.
"It sounds ridiculous, but I feel emotional about it," she said. "This is what we do from September to Christmas. We become obsessed by the foxtrot."
However, Winkleman insisted that the arrival of Arthur made it worth leaving Strictly behind.
"I'm obsessed with the other two [children] but there's something about him," she said. "I could talk about him until your ears bleed... I can barely breathe. I just want to go and get in the car, get home, get naked and cuddle him."