In our unit, if a nurse has formed a supportive relationship with the family (and has expressed a willingness to be notified), we will often call them to come in and be there during the death if possible. This is helpful for the nurse and the family. You might mention this option to the manager to prevent this kind of thing from happening again.
While death is certainly a very real part of the job, we shouldn't expect people to just take the next assignment and move on as if nothing has happened.... especially if this was an unexpected death or if the nurse had been close to the baby / family. We want to support and encourage that kind of caring... not make it more difficult.
As the responder above mentioned, you may also want to seek personal counseling, see a doctor or mental health care provider, speak to your manager or an experienced nurse you trust, or see the hospital chaplain. All these people will have dealt with this response and these feelings previously and should be helpful and empathetic.
Have you considered writing a letter to the baby's family? You could say what you liked about the baby, share a memory -- for example you could talk about her eyes, they way they looked deep into yours, like you shared here. Remember to frame everything you say positively -- "she had a way of looking right into my heart"... instead of "she was begging me for help with her eyes"... (of course... I"m sure you realize that!) These families often feel like no one even got a chance to know their child... and to know that someone had a relationship with her, that they knew her personality and cared about her is VERY comforting. Saying "I'm so sorry this happened" -- is ok! Some nurses hesitate to do that, wondering if that expresses some type of responsibility on their behalf or by the hospital -- but you're simply stating that the end result of this situation was very sad and that you are empathizing with the family's pain and loss. I'm sure a note from you would become one of their treasured belongings....and I bet it would go a long way to giving you that sense of closure that you need.
Also -- does your hospital have a service where they remember the babies lost each year? We have one and sometimes, especially if the families choose not to attend, a nurse will attend in honor of a special patient. All who have done that have said how meaningful it was to them to participate and to continue to recognize that special relationship. Other things you can do as a memorial to her might help as well.... maybe make a donation in her honor?, Buy a special blanket or mobile for the unit?, Purchase hats or socks for each NICU baby? You could include a tag stating it was in her honor if you'd like... or just know in your heart the reason.
Hang in there... find ways to share your feelings, that will help so much! Sending you hugs!