Missy found out about Clara's death and Clara being taken out of her time stream after ensnaring the Doctor in yet another trap of hers. The Doctor speaking of the time he knew a Clara, but couldn't remember anything about her appearance, confused Missy. Then Missy realized something must've happened to the Doctor to cause him to forget Clara, to stop her plans of causing chaos through Clara and the Doctor traveling together. The woman who called herself Me did warn her someone would stop Missy's plans of spreading chaos around the universe.
Missy thought about Clara's loss after the Doctor escaped her trap. Missy didn't want to admit she had a soft spot for Clara, but she did. If Missy hated Clara, she would've killed her outright instead of torturing her and making her a pawn to get the Doctor to feel how she felt for centuries. She even thought she would've stepped in if the Doctor did attempt to shoot Clara while she was in the Dalek shell.
Missy wasn't one for companions, but a part of her wondered what would've happened if Clara and Missy traveled together. Missy was sure the Doctor would get Clara to be a part of his "army," but not before they caused havoc around the universe.
But Missy didn't have to say goodbye like the Doctor did. Clara might be dead, but there was still a part of her out there in the galaxy. Missy could always find her, wherever Clara was.