What is the meaning of "Hachras"?
Rashi: This is like Nichras. Hei with Chataf Kamatz is in place of Nun, e.g. "v'Chayas ha'Sadeh Hashlemah Lach" (Iyov 5:23). Radak - the locusts cut it off. If grain and wine ceased, how will they bring Minchah and Nesech to the Beis ha'Mikdash, and they lack what to eat and drink?! 1
Radak: Hachras is masculine, even though Minchah is feminine, for the matter (Korban - Minchah and Nesech) is masculine. The same applies to "Asher Ye'aseh me'Eleh" (Vayikra 2:8), "Ye'aseh Melachah" (Shemos 31:15; the subjects are Minchah and Melachah).
Why do the Kohanim mourn?
Radak: They ate from Hashem's table - and there is not [anything on His table now].
Malbim: They mourn that Minchah and Nesachim are cut off from Beis Hashem.