The parents, who asked not to be identified, said they would always treasure their short time with 15-month-old Eden, who was found in her cot choking on the cord at their Quakers Hill home on Tuesday evening.
Eden was taken to the Children's Hospital at Westmead but died later that night.
Her death came just five days after a 16-month-old girl died in almost identical circumstances in Hornsby.
Eden's parents urged other parents to take action to prevent the heartache they were experiencing.
"It is absolutely unfathomable that a tragedy like this could happen ... We encourage every parent to check their child's cot for even the slightest danger," they said.
Police said they were called to the home on Hillcrest Avenue in Quakers Hill at 6.25pm on Tuesday after a child was found unconscious in her cot.
Paramedics and a CareFlight doctor worked to resuscitate Eden before taking her to hospital.
KidSafe executive officer Christine Erksine said parents were not always aware of the dangers posed by blind cords.
"It's just one of those horrible accidents that can happen," she said.
"It's just something you wouldn't be aware of.
"At least 11 children died in Australia between 2001 and 2008 after being caught in blind cords, the Australian Competition and Consumer Commission said.
The Commission recommends tying cords out of reach of children.