This question touches the painful subject of suicide, for that is the real meaning of the word "Release." Rosemary chooses to inject herself with a lethal substance rather than keep on living under the burden of her call or "Appointment."
As Rosemary was his own daughter, the Giver feels grief beyond sorrow or remorse. This event is critical in that it paves the way for his actually doing something to help the Community escape from its own ignorance. He cooperates with Jonas in his plan to escape with Gabriel so that the collective memory he harbours will come back to the people instead.
Although Lowry does not come out with any overt statement, she leads the reader to think that Rosemary (the next 'Giver' in line) might also be the Giver's genetic daughter (and Jonas and even Gabriel, too, his offspring.) The common denominator they share are their pale blue eyes, a very rare trait among the Community members.
He is sad because she was his "daughter." We are led to believe that she may be his biological daughter because of the eye color (which would mean that Jonas and Gabriel could also be his family) and since he is the one holding all of the memories, he may know this. The giver wants to be with her after everything that he plans to accomplish with Jonas is done.