In the very first Avengers movie, Loki taunts Natasha by telling her that he knows all the horrors that she committed in the name of Hydra. That being said, he had the Tesseract and even without it he was able to use magic.
Is there a chance that he knew about Antonia Dreykov being alive as well as her father? If that's the case, do you think that he would have used that knowledge to mess with Natasha's head even further if given the chance, since he was technically under the same conditioning that she was?