Quaid said he learned of the error the morning after it happened when he went to Cedars-Sinai Medical Center to visit his children, the Los Angeles Times reported.
"Our kids could have been dying, and we wouldn't have been able to come down to the hospital to say goodbye," Quaid told the Times in an exclusive interview.
The actor recalled how he was met at the door of the children's hospital room by a pediatrician, a nurse and a representative of the hospital's risk management department, and told about the heparin overdose and what its effects are. He was also informed his children were given an antidote.
Quaid and his wife, Kimberly, also said they suspect someone at the hospital leaked information to the media and, because of that, family members they tried to shield from the news heard the story after TMZ.com reported it.
After spending 11 days in intensive care, however, little Thomas and Zoe appear to have made a full recovery, he said, adding, "We have our babies back, and they seem to be doing great."