The Ksav Sofer writes that the sorrow to which the verse refers was the sadness felt for Moshe’s death (Adar 7). This is because people at the time feared that the Torah would be forgotten. This is what the Talmud (Bava Basra 75b) implies by quoting the leaders of the time as saying, “Woe onto us that Moshe’s face is like the sun, and Yehoshua’s is like the moon!” They were, however, incorrect in their estimations, as Yehoshua proved to be a faithful conductor of Moshe’s teaching, as testified to in the Mishna (Avos 1:1).
Furthermore, the Jews’ re-acceptance of the Torah on Purim, as seen from the words kimu v’kiblu (“they established and accepted”) (Esther 9:27) demonstrates that the Torah of Moshe did not die (chas v’Shalom) with him.
Furthermore, the Maharal opines that since Adar is the end of the annual cycle of months, Adar would spell the end of the Jews.